Methods for plasticizing poly(ethylene furanoate) films by water sorption

ABSTRACT

This disclosure provides an investigation of the kinetic uptake properties of water in amorphous PEF and PET across the entire water activity interval at various temperatures, and also investigates the corresponding equilibrium uptake properties at the same conditions. Uptake data were measured using three independent and complementary methodologies, and excellent agreement was observed among all three methodologies. Accordingly, this disclosure provides for methods of plasticizing poly(ethylene furanoate) film by cold water sorption, and provides a plasticized poly(ethylene furanoate) (PEF) film made according to the disclosed methods. Methods for making thin films of PEF are also provided.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a 35 U.S.C. § 371 National stage application of International Patent Application No. PCT/US2015/050244, filed Sep. 15, 2015, which claims priority benefit of U.S. Provisional Application No. 62/051,168, filed Sep. 16, 2014, which is incorporated by reference herein in its entirety.

FIELD OF THE DISCLOSURE

The present disclosure is generally related to water sorption by poly(ethylene furanoate), particularly poly(ethylene furanoate) films.

BACKGROUND OF THE DISCLOSURE

Interest in poly(ethylene furanoate) (PEF) polyesters, also termed poly(ethylene-2,5-furandicarboxylate), as a potential replacement for poly(ethylene terephthalate) (PET) has increased in recent years, largely due to the ability to synthesize PEF from bio-based sources. Generally, the differences between the physical-chemical behavior of PEF versus PET has presented substantial challenges to the wholesale use of PEF in conventional PET-based applications. For example, compared to standard commercial grade poly(ethylene terephthalate), PEF polyesters often possess lower crystallinity, crystallize at slower rates, and are entangled to a lesser extent.

In order to develop a roadmap for increased use of PEF, particularly as a prospective PET replacement, it has been of interest to examine the differences in the fundamental materials and engineering aspects of PEF versus PET. In particular, a better understanding of the thermodynamic and kinetic differences between PEF and PET in their water sorption properties and other factors that affect plasticization would be useful.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows initial equilibrium water sorption values for water at 35° C. in PEF (diamonds) and PET (circles). Solid data points represent measurements from the automated VTI system, while hollow points represent measurements from the quartz spring (QS) apparatus.

FIG. 2 shows equilibrium sorption values for water at 35° C. in PEF (diamonds) and PET (circles) at 35° C. during the first sorption cycle. Solid data points represent measurements from the automated VTI system, while hollow points at unit activity represent gravimetric sorption data measured in liquid water (LW).

FIG. 3 shows equilibrium sorption values for water at 35° C. in PEF (diamonds) and PET (circles) at 35° C. during the first sorption cycle. Solid data points represent measurements from the automated VTI system, while hollow points at unit activity represent gravimetric sorption data measured in liquid water (LW).

FIG. 4 shows interaction parameters for water at 35° C. in PEF (diamonds) and PET (circles) at 35° C. Solid data points represent measurements from the automated VTI system, while hollow points represent gravimetric sorption data measured in liquid water (LW). Lines represent model fits from Equation 4.

FIG. 5 shows that the onset of clustering/plasticization is realized when the quantity ϕ₁G₁₁/V ₁ is greater than zero.

FIG. 6 shows sorption hysteresis at 35° C. for PEF recorded using the automated VTI sorption system. Filled and hollow circles represent the initial sorption and desorption cycle, respectively, while filled and hollow triangles represent the second sorption and desorption cycle, respectively. Lines are drawn to aid the eye and do not represent model fits.

FIG. 7 shows sorption hysteresis at 35° C. for PET recorded using the automated VTI sorption system. Filled and hollow circles represent the initial sorption and desorption cycle, respectively, while filled and hollow triangles represent the second sorption and desorption cycle, respectively. Lines are drawn to aid the eye and do not represent model fits.

FIG. 8 shows a semi-logarithmic van't Hoff plot of water sorption at 0.2 activity in amorphous PEF (filled diamonds) and amorphous PET (hollow circles). Lines represent the van't Hoff representation from Equation 9.

FIG. 9 shows water uptake data at 35° C. for PEF (diamonds) and PET (circles) measured during sorption between 0-0.4 activity using the quartz spring system. Data are plotted versus a non-dimensional time, with the corresponding Fickian fit from Equation 11. Respective D_(Avg) values are provided in the supplemental information.

FIG. 10 shows sorption/desorption data for water in PEF at 35° C. from the automated VTI instrument. Both (a) and (b) contain complementary kinetic and equilibrium sorption data for PEF, where the equilibrium sorption data are summarized in FIGS. 6 and 7 of reference [15].

FIG. 11 shows water uptake data at 35° C. measured by the automated VTI system during sorption between 0-0.1 activity (a) and 0.1-0.2 activity (b). Dashed lines represent the Fickian fit from Equation 11, while solid lines represent the BH-Exp fit from Equation 17. Model parameters are as follows: (a) Fickian (D_(Avg)=1.55×10⁻⁹ cm²/s), BH-Exp (D_(Avg)=1.83×10⁻⁹ cm²/s, ϕ_(F)=1, τ_(R)=not used, τ_(S)=1820 s), and for (b) Fickian (D_(Avg)=2.09×10⁻⁹ cm²/s), BH-Exp (D_(Avg)=2.14×10⁻⁹ cm²/s, ϕ_(F)=1, τ_(R)=not used, τ_(S)=214 s).

FIG. 12 shows kinetic sorption data from FIG. 2a for water in PEF at 35° C. measured by the VTI system. Lines represent model fits from Equation 17 corresponding to sorption (solid) and subsequent desorption (dashed), while experimental data are represented in grey. The sorption intervals are labeled in each respective graph.

FIG. 13 shows kinetic sorption data from FIG. 2b for water in PET at 35° C. measured by the VTI system. Lines represent model fits from Equation 17 corresponding to sorption (solid) and subsequent desorption (dashed), while experimental data are represented in grey. The sorption intervals are labeled in each respective graph.

FIG. 14 shows D_(Avg) values from Equation 17 for water in PEF at 35° C. measured from the VTI system. Sorption (solid circles) and subsequent desorption values (hollow circles) are plotted at the midpoint activity of the respective sorption interval, and correlate with model fits to the data in plots (a)-(j) from FIG. 12.

FIG. 15 shows D_(Avg) values from Equation 17 for water in PET at 35° C. measured from the VTI system. Sorption (solid circles) and subsequent desorption (hollow circles) values are plotted at the midpoint activity of the respective sorption interval, and correlate with model fits to the data in plots (a)-(j) from FIG. 13.

FIG. 16 shows sorption and desorption averaged diffusion coefficients (D_((s+d)/s)) measured from the VTI system for water in PEF (diamonds) and PET (circles) at 35° C.

FIG. 17 shows diffusion coefficients from FIG. 16 versus equilibrium water concentration at 35° C. for PEF (diamonds) and PET (circles). Lines reflect model fits from Equation 19, and respective model parameters are included in the text.

FIG. 18 shows a plot of ϕ_(F) from Equation 17 for water at 35° C. in PEF (solid diamonds) and PET (hollow circles) measured by the VTI system for sorption (a) and desorption (b).

FIG. 19 shows a plot of τ_(R) from Equation 17 for water at 35° C. in PEF (diamonds) and PET (circles) measured by the VTI system for sorption (filled) and desorption (hollow). Values of τ_(R) are only provided for values of ϕ_(F)<1 from FIG. 18.

FIG. 20 shows a plot of τ_(S) from Equation 17 for water at 35° C. in PEF (diamonds) and PET (circles) measured by the VTI system for sorption (solid) and desorption (hollow). Recall that τ_(S) is an instrumental parameter, and does not reflect intrinsic properties of the polymer.

FIG. 21 shows diffusion coefficients for water in PEF at 35° C. Data for the first sorption cycle (hollow diamonds) and second sorption cycle (hollow circles) represent values of D_((s+d)/2), while the solid circle represents D_(Avg) measured during sorption from 0-1 activity. Values are plotted at the midpoint of their respective activity intervals.

FIG. 22 shows diffusion coefficients for water in PET at 35° C. Data for the first sorption cycle (hollow diamonds) and second sorption cycle (hollow circles) represent values of D_((s+d)/2), while the solid circle represents D_(Avg) measured during sorption from 0-1 activity. Values are plotted at the midpoint of their respective activity intervals.

FIG. 23 shows kinetic sorption data during sorption between 0-1 activity for water at 35° C. in PEF (a) and PET (b). Lines represent the Fickian model fit from Equation 11, and corresponding D_(Avg) values for PEF and PET plotted in FIGS. 13 and 14, respectively. Both (a) and (b) reflect normalized data from four separate sorption experiments.

FIG. 24 shows temperature-dependent diffusion coefficients for PEF (diamonds) and PET (circles) measured during sorption between 0.1-0.2 activity. Lines reflect model fits from Equation 20.

FIG. 25 shows D_(Avg) values for water in PEF (diamonds) and PET (circles) measured at 35° C. by the automated VTI system (solid points) and the manual quartz spring system (QS, hollow points).

FIG. 26 shows diffusion coefficient data for water at 35° C. in PEF (a) and PET (b) measured by the VTI instrument (taken from FIGS. 14 and 15 of the kinetic sorption portion (Part 2) of this disclosure [1]). The solid lines represent the optimized fits from Equation S3 (F≈0) with D_(D)=2.6×10⁻⁹ cm²/s for PEF and D_(D)=1.5×10⁻⁸ cm²/s for PET. The dashed lines represent 0.6 activity.

DISCLOSURE OF THE INVENTION

This disclosure provides, among other things, a comparison of the water sorption properties in poly(ethylene furanoate) (PEF) compared to poly(ethylene terephthalate) (PET), and demonstrates new methods for plasticization of PEF by cold water sorption. This disclosure is provided in two (2) Sections: Part 1, drawn to the thermodynamics of water sorption, that is, “equilibrium sorption”; and Part 2, drawn to the kinetics of water sorption, that is “kinetic sorption”. It is to be understood that the following detailed description is exemplary and explanatory only and is not restrictive.

In the following description, numerous specific details are given to provide a thorough understanding of embodiments. The embodiments can be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the embodiments.

Reference throughout this specification to “one embodiment,” “an embodiment,” or “embodiments” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

Part 1. Equilibrium Sorption

Overview

Equilibrium water sorption properties of amorphous poly(ethylene furanoate) (PEF) and amorphous poly(ethylene terephthalate) (PET) were studied at 35° C. over the entire water activity range. PEF exhibits a largely increased equilibrium water sorption capacity of ˜1.8× averaged over the entire concentration range compared to PET, resulting from substitution of the non-polar phenyl ring in PET with the polar furan ring in PEF. Both polyesters exhibit dual-mode sorption up to ˜0.6 activity, after which the onset of plasticization produces a noticeable upturn in concentration vs. activity for both polyesters. Excellent agreement was observed between three independent sorption measurement techniques, thereby providing a consistency check for the reported data. Sorption measurements performed at 15, 25, 35, and 45° C. allowed estimation of the effective enthalpy of water sorption for both polyesters, which were similar to the enthalpy of condensation for pure water. The current disclosure demonstrates, among other things, how structure affects sorption and transport properties in these two important polyesters.

1. Introduction

Understanding the sorption and transport behavior of water in polymeric materials is important for barrier applications involving contact with liquid water and high activity water vapor. Moisture can have significant detrimental effects on mechanical, thermal, and barrier properties of such polymers [1-4], due primarily to plasticization of the matrix. Recent advancements have enabled cost-effective production of poly(ethylene furanoate) (PEF), a new biologically sourced polyester showing enhanced performance compared to petroleum-based PET [5]. Currently, no data exists in the literature regarding the water sorption properties of PEF compared to PET; however, detailed understanding of these properties is needed before PEF can be integrated into the global polyester market.

Previous research into the fundamental properties of PEF has focused on lab scale synthesis and characterization of thermal, mechanical, and crystallization properties, among others [6-10]. Recent research examined performance enhancements for PEF compared to PET related to differences in segmental mobility, which result from differences in ring type and connectivity and the subsequent relative ease of ring flipping mechanisms [11]. Additional work has focused on understanding the fundamental oxygen sorption and transport properties of PEF at various temperatures, where the significantly reduced oxygen permeability for PEF compared to PET was again related to differences in segmental mobility [12]. Water sorption in polyesters is notably more complex than oxygen sorption, since water is more condensable and shows greater interaction with the polymer matrix. Consequently, water is known to plasticize the PET matrix, thereby resulting in a reduction in glass transition temperature [13].

This disclosure provides a detailed investigation of the equilibrium water sorption properties in amorphous PEF and PET at 35° C. via three different gravimetric techniques, while complementary kinetic sorption data are provided in Part 2 [14]. Compared to PET, PEF exhibits a 1.8× higher water sorption capacity averaged over the entire water activity range. Increased water uptake for PEF reflects the substitution of the non-polar phenyl ring in PET with the polar furan ring in PEF, also in part from the higher free volume in PEF compared to PET [11]. Related observations were made by Rueda et al. [15, 16] for water solubility in poly(ethylene naphthalate) (PEN), where the authors explained increased water uptake for PEN compared to PET based on respective differences in free volume.

Both polyesters used in the current disclosure exhibited so-called “dual-mode sorption” reflected by concavity in the isotherms up to ˜0.6 activity, after which distinct upturns occurred at high water activity. Morphological changes induced at high activity are indicated for both polyesters via distinct sorption hysteresis. These hysteretic responses correlate with the presence of non-Fickian relaxations during sorption at high activity described in Part 2 [14]. Excellent agreement is observed in sorption values over the entire water activity range for all three independent methods, thereby illustrating internal consistency for the reported data. Additional measurements performed at different temperatures allowed calculation of the enthalpy of water sorption in both polyesters, which can be combined with the diffusion activation energy presented in Part 2 to estimate values for the activation energy of water permeation in both polyesters [14]. The current disclosure, in combination with our kinetic sorption counterpart, presents the first in-depth analysis of water transport in PEF and sets out its specific utility.

2. Experimental

2.1 Materials and Film Preparation

Both poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET) were provided by The Coca-Cola Company and are identical to the materials considered in our previous work [11, 12]. Structural information for both PEF and PET is provided in Table 1. An identical melt-press/quench methodology used in prior work [11] was utilized to prepare amorphous polyester films for sorption testing. De-ionized water was used for all sorption testing, and the nitrogen (UHP grade) carrier gas utilized in the automated sorption system was provided by Airgas (Radnor, Pa.).

TABLE 1 Structural information for poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET). Polymer Structure Poly(ethylene furanoate)

Poly(ethylene terephthalate)

2.2 Sorption Measurements

Gravimetric sorption measurements were recorded for both polyesters between 0-0.95 activity on a TA VTI-SA+ automated vapor sorption analyzer (TA Instruments, New Castle, Del.). This system provides a humidified nitrogen stream by mixing a separate wet and dry stream, which are controlled by two individual mass flow controllers. The resulting humidified stream flows through a dew point analyzer, which continuously measures the water content in the stream and provides feedback to the instrument to allow for automated control. After exiting the dew point analyzer, the humid stream passes over a quartz basket containing the polymer sample, which is attached to a sensitive microgram balance (accuracy±0.1%). Once the mass uptake for a given activity has reached equilibrium, the system automatically proceeds to the next programmed activity step. Equilibrium is realized when the mass uptake over a specified time interval falls below a threshold limit, e.g. 0.0015% mass change in 99 minutes. Multiple equilibration intervals were needed at high activity for both polyesters due to the protracted gradual increase in water uptake resulting from non-Fickian relaxations. Film samples with an approximate thickness of ˜160 microns were initially dried in the instrument at 45° C. until constant mass was achieved, prior to commencing sorption. Interval sorption measurements were recorded using water activities ranging from 0-0.9 in increments of 0.1, along with a final value of 0.95. Both sorption and desorption interval measurements were recorded over the entire activity range, followed by a second set of interval sorption and desorption measurements recorded at 0.3, 0.6, and 0.95 activity. The presence of long-term non-Fickian relaxations prevented attainment of true equilibrium mass uptake between the sorption values of 0.7-0.95. However, as will be shown later in this part and in Part 2 of this disclosure [14], the overall implications of this second order effect appear to be negligible.

The McBain quartz spring technique [17] was also used to manually record sorption measurements at 35° C. between the range of 0-0.6 activity. The apparatus has been described in other work [18-20]. Film thickness values for different samples ranged from 50-150 microns. Sorption values measured via this technique provide a consistency check when compared to the values determined from the automated VTI system. The McBain measurements were recorded via integral sorption as opposed to the alternative interval sorption methodology used in the VTI instrument.

Both the automated VTI sorption system and the manual quartz spring system are unable to measure water sorption data at complete saturation (i.e. unit activity) due to water condensation. To circumvent this problem, measurements at unit activity were made by submerging thick polymer samples in de-ionized liquid water at 35° C. and periodically removing the samples and recording their masses on a sensitive microgram balance (Mettler Toledo XP6). The samples were sufficiently thick (i.e. ˜500 microns for PEF, ˜890 microns for PET) so that desorption during the weighing step was insignificant. Mass measurements were recorded until constant uptake was achieved, and the corresponding values represent the integral sorption step between zero and unit activity. Four replicate samples were tested for both polyesters to allow calculation of uncertainty limits via the standard error. Thickness values for the polymer films were measured on the initially dry samples and again after exposure to liquid water at 35° C. for approximately four months to quantify the effect of swelling. This gravimetric sorption technique allows for completion of the sorption data set by covering the entire activity range from zero to unit activity. The water uptake measured via this technique allowed determination of the true equilibrium uptake at unit activity, and provides a consistency check for data obtained using the other sorption techniques.

3. Results and Discussion

3.1 Initial Sorption at 35° C.

Vapor sorption in glassy polymers is often characterized by dual-mode sorption at low activities, and can be described by the dual-mode model [21] in Equation 1. Such data exhibit concavity in concentration with respect to penetrant pressure, and resemble the dual-mode sorption behavior for non-condensable gases (i.e. oxygen [12] and nitrogen [22]) in glassy polymers.

$\begin{matrix} {C = {{k_{D}p} + \frac{C_{H}^{\prime}{bp}}{1 + {bp}}}} & (1) \end{matrix}$

In Equation 1, p represents pressure (atm), k_(D) is the Henry's law solubility coefficient (cm³STP/cm³Poly·atm), C_(H)′ is the Langmuir capacity constant (cm³STP/cm³Poly), and b is the Langmuir affinity parameter (atm⁻¹). Water sorption data at 35° C. is plotted in FIG. 1 up to 0.6 activity for PEF (diamonds) and PET (circles), and reflects data measured from both the VTI system (solid points) and the quartz spring system (hollow points). Dual-mode model fits from Equation 1 are plotted via the solid lines in FIG. 1, and the corresponding model parameters are listed in Table 2. Excellent agreement between data measured from the two independent sorption methodologies provides a consistency check for the reported data. Noticeable deviation from dual-mode behavior was observed after 0.6 activity, and will be discussed later in the document.

TABLE 2 Dual-mode parameters from Equation 1 for water sorption and subsequent desorption in PEF and PET at 35° C. The uncertainty limits represent the standard error as determined from the curve fitting program. Parameters for desorption are described in Section 3.3 k_(D) k* (cm³STP/ C_(H)′ (cm³STP/ Activity cm³ Poly · b (cm³STP/ cm³Poly · Range Sample atm) (atm⁻¹) cm³ Poly) atm) Sorp- PEF 354 ± 7  141 ± 30  3.07 ± 0.4 787 ± 110 tion PET 237 ± 16 88.7 ± 180 0.599 ± 0.9  290 ± 140 (0-0.6) Desorp- PEF 421 ± 25 141^(a) 5.82 ± 1.7 1240 ± 297  tion PET 274 ± 7     88.7^(a) 1.62 ± 0.6 418 ± 297 (0.95-0) ^(a)The value of b from sorption was fixed in the determination of desorption parameters.

The sorption values reported in FIG. 1 for water in amorphous PET exhibit excellent agreement with the results from various studies in the literature on amorphous PET [1, 15, 23]. Water sorption results from semicrystalline PET can be compared to the current amorphous data via the relationship S=S_(a)X_(a) validated by Lasoski and Cobbs [24], where S represents the solubility (analogous to C or k_(D) from Equation 1) and X_(a) represents the amorphous fraction of the polymer. Comparisons performed in this manner reveal that the data for amorphous PET in FIG. 1 are slightly lower than the normalized semicrystalline data from various studies [25, 26]. This behavior can be rationalized by the likelihood of increased sorption in the dedensified rigid amorphous fraction surrounding the immediate vicinity of the crystallites in the semicrystalline samples [27].

The Langmuir affinity parameter (b) value of 88.7 atm⁻¹ for water in amorphous PET reported in Table 2 agrees well with the value of 94.6 atm⁻¹ reported by Shigetomi et al. [26] for water in semicrystalline PET. This result is expected, since the impermeable crystallites should ideally not affect the thermodynamic interaction between the penetrant and polymer sites within the amorphous domain [21]. The k_(D) and C_(H)′ parameters for the semicrystalline sample, however, will be affected by the presence of crystallinity [21]. A value of 237 cm³STP/cm³Poly·atm for k_(D) in this disclosure (Table 2) is similar in magnitude to the amorphous value of 285 cm³STP/cm³Poly·atm by Fukuda et al. [23] and the normalized semicrystalline value of 284 cm³STP/cm³Poly·atm from Shigetomi et al. [26]. In contrast to b and k_(D), the value of C_(H)′ in this disclosure differs significantly from the value reported by Shigetomi et al. [26]. This difference can be explained by potential variations in either sample processing [18], prior thermal history, or from differences in crystallinity [21].

FIG. 1 reveals that water is noticeably more sorptive in PEF compared to PET. This result can be interpreted via the dual-mode parameters listed in Table 2, which show a larger k_(D) for PEF compared to PET. The interaction parameter (b) for PEF is also significantly larger than the value for PET, thus indicating a stronger interaction between water and the polymer matrix. This behavior is expected, especially when considering the polar nature of the furan ring in PEF compared to the non-polar phenyl ring in PET. Values of b for water in both polyesters are also significantly larger than the respective values for oxygen [12], which is attributable to large differences in critical temperature and the Lennard-Jones force constant for the two penetrants [19]. Aside from k_(D) and b, a larger C_(H)′ is observed for PEF compared to PET and likely originates from the larger fractional free volume (FFV) for PEF [11].

High activity vapor sorption in glassy polymers is often characterized by an upturn in solubility with respect to activity [18, 19, 28-30]. Such isotherms have been described using the modified dual-mode model proposed by Mauze and Stern [31] or more recently by the unified dual-mode model proposed by Guo and Barbari [32]. Satisfactory description of the data can also be provided by the Flory-Huggins representation developed for sorption in rubbery materials via Equation 2 [33], despite both polymers existing in the glassy state at 35° C. In Equation 2, p is the penetrant pressure, p₀ is the saturation vapor pressure, ϕ₁ is the volume fraction of the penetrant, and χ is the “effective” Flory-Huggins interaction parameter. Calculation of ϕ₁ can be achieved through Equation 3 [28], where V₁ is the molar volume of water at 35° C. (18.02 g/mol divided by 0.9941 g/cm³) and C is the concentration (cm³STP/cm³Poly).

$\begin{matrix} {{\ln\mspace{11mu}\left( \frac{p}{p_{0}} \right)} = {{\ln\;\phi_{1}} + \left( {1 - \phi_{1}} \right) + {\chi\left( {1 - \phi_{1}} \right)}^{2}}} & (2) \\ {\phi_{1} = \frac{C\left( {V_{1}\text{/}22414} \right)}{1 + {C\left( {V_{1}\text{/}22414} \right)}}} & (3) \end{matrix}$

Use of Equation 2 coupled with a constant interaction parameter signifies the ideal case of random mixing between penetrant and polymer [34-36]. Sorption data for iso-propanol, ethanol, and methanol in PET are well described via this simplified methodology [18, 19]. More complicated sorption cases, however, require a concentration dependant expression for χ and can suggest deviations from random mixing. Equation 4 represents a simple model for capturing the concentration dependence of χ, where χ₀, χ₁, and χ₂ are constants associated with the model fit [37, 38]. χ=χ₀+χ₁(1−ϕ₁)+χ₂(1−ϕ₁)²  (4)

Water sorption data for both polyesters are provided over the entire activity range in FIG. 2 via units of concentration (cm³STP/cm³Poly) and in FIG. 3 via units of wt % (g H₂O/g Poly), along with the Flory-Huggins fit from Equation 2 coupled with a concentration-dependent interaction parameter. A graph of the Flory-Huggins interaction parameter vs. volume fraction water is provided in FIG. 4, with model parameters from Equation 4 for PEF as follows: χ₀=−2273±157, χ₁=4623±318, and χ₂=−2347±161. Corresponding model parameters for PET are: χ₀=−3373±277, χ₁=6800±558, and χ₂=−3424±281. The solid points in FIGS. 2 and 3 represent data measured via the automated VTI sorption system, while the hollow points represent data measured in liquid water.

As mentioned previously, the solid data points in FIGS. 2 and 3 measured between 0.7-0.95 activity from the automated VTI system are slightly lower than the true equilibrium values due to the presence of long-term non-Fickian relaxations at high activity [14]. Similar termination of sorption before achieving true equilibrium was also done by Berens, who noted that determination of the true equilibrium sorption isotherm at high activity “would be excessively time-consuming” [39]. The differences between the equilibrium values reported in FIGS. 2 and 3 between 0.7-0.95 activity and the true equilibrium values are minor, due to small “extra” relaxation-induced uptake associated with the non-Fickian relaxations [14]. Further verification of this notion is provided by excellent agreement of the data in FIGS. 2 and 3 (solid points) with the data recorded at unit activity and true equilibrium (hollow points).

From FIG. 2, it is apparent that the water uptake data in both PEF and PET exhibit an upturn in concentration at high activity and that the Flory-Huggins model coupled with a concentration-dependent x interaction parameter accurately describes the data. A distinct sorption upturn at high activity for PET has also been reported for both amorphous [23] and semicrystalline PET samples [25, 40], however the degree of upturn in the semicrystalline samples is less significant than in the current disclosure due to the presence of impermeable crystallites acting to stabilize the matrix against swelling. Additional studies have reported linear sorption isotherms for both amorphous [1, 13] and semicrystalline PET [41], which contrasts to the trend observed in the current disclosure. The water sorption value for PET measured in liquid water (hollow circle in FIG. 3) agrees well with the normalized semicrystalline value reported by Park [42] using a similar measurement methodology. Deviations from dual-mode equilibrium behavior above 0.6 activity correlate with the onset of non-Fickian kinetic relaxations observed in FIGS. 4 and 5 of Part 2 for both polyesters [14].

Similar to PET, PEF also exhibits a distinct upturn in concentration at high activities as seen in FIGS. 2 and 3. As mentioned previously, higher water solubility in PEF compared to PET is expected due to the increased polarity of the furan ring compared to the non-polar phenyl ring in PET. The upturn for both polyesters signifies the presence of either water clustering, plasticization, or both, and will be discussed in the next section.

The polymer-solvent interaction parameters plotted in FIG. 4 reveal a distinct concentration dependence for both polyesters. In the context of previous work [34-36], this dependence can reveal a departure from random mixing (i.e. clustering) in the water/polyester system as specified by Flory-Huggins theory. Validation of the interaction parameters from FIG. 4 can be investigated using the solubility parameter (δ) framework, which utilizes the relationship shown in Equation 5 [43].

$\begin{matrix} {\chi \approx {0.34 + {\frac{V_{s}}{RT}\left( {\delta_{1} - \delta_{2}} \right)^{2}}}} & (5) \end{matrix}$

In Equation 5, subscripts refer to the penetrant (1) and polymer (2), V_(S) is the molar volume of the penetrant, R is the universal gas constant, and T is the temperature in Kelvin. Using this framework, it is possible to predict values of the polymer-solvent interaction parameter based solely on the independent properties of the polymer and solvent. While the solubility parameters for PET and PEF are available via group contribution methods [43], considerable inaccuracy exists in estimation of δ₁ for water. In fact, the behavior of water can vary based on the local environment, thereby rendering predictions using Equation 5 somewhat speculative [44]. Qualitative applicability of Equation 5, however, is still justified in comparing polymers with similar values of δ₂ due to the expected similarity of δ₁ for water.

The solubility parameter for PET as estimated by van Krevelen [43] is 20.5 (MJ/m³)^(1/2) and the average value of χ from FIG. 4 for PET over the entire activity range is 3.47. A value of 3.69 for the average χ for poly(methyl acrylate) (PMA) was reported by Williams et al. [35]. This value is consistent our value of χ for PET, since the solubility parameter for PMA (19.9 (MJ/m³)^(1/2) [43]) is similar to that reported for PET. An estimate of the solubility parameter for PEF, and polymers in general, can be obtained from the square root of the cohesive energy density (i.e. δ₂≈(E_(coh))^(1/2)) [43]. Cohesive energy density values of 560 J/cm³ for PEF and 540 J/cm³ for PET are available from prior work [12], and exhibit a slightly larger δ₂ value for PEF compared to PET. This trend is also reflected experimentally by the average χ value of 2.92 for PEF, which is lower than the value of 3.47 for PET. A lower χ value for PEF therefore suggests a higher degree of compatibility with water, which can easily be rationalized when considering the increased polarity of PEF compared to PET.

3.2 Clustering Vs. Plasticization

A positive deviation from dual-mode or Henry's law sorption at high vapor activities can indicate simple swelling or clustering, which is the nonrandom distribution of a penetrant within the polymer matrix [34, 45]. Plasticization is indicated when the upturn in solubility accompanies a simultaneous increase in diffusion coefficient, thus giving evidence for increased segmental mobility. Alternatively, clustering is indicated when the upturn in solubility accompanies a decrease in diffusion coefficient, which results from an increase in the effective diameter of the diffusing water (i.e. water molecules cluster together) [35]. Permeation experiments can also be used to differentiate between the two phenomena, as plasticization yields an increase in permeability at high activity while clustering exhibits a more or less constant permeability with increasing activity. Both plasticization [45-48] and clustering [28, 34-36, 49-52] phenomena have been reported for a wide range of penetrants and polymers.

Besides clustering, penetrant plasticization in glassy polymers is quite common. Numerous studies have focused on carbon dioxide-induced dilation and plasticization in polymer membranes [53-61], since such behavior can compromise the separation efficiency of the membrane. Several recent studies have examined related plasticizing effects via various computer modeling techniques [62-65]. Using molecular dynamics simulations, Neyertz and Brown determined that the free volume within a polyimide increased with carbon dioxide-induced swelling [65]. A further study by the same authors examined both para- and meta-substituted polyimide isomers, and concluded that the swelling behavior upon carbon dioxide sorption resulted from localized relaxations in the respective matrices rather than larger structural changes [66]. Aside from carbon dioxide, which typically plasticizes glassy polymers at relatively high pressures [67], water and organic vapors are also prone to induce plasticization effects in various polymers as evidenced by sorption hysteresis due to increased condensability and interactions with the matrix [18, 45-47, 52, 68].

The onset of clustering or plasticization can be qualitatively determined using the analysis proposed by Zimm and Lundberg [69], which interprets the shape of the equilibrium sorption isotherm in terms of a so-called cluster integral (G₁₁). Equation 6 reflects their methodology, where a₁ is the activity of the penetrant (i.e. p/p₀), ϕ₁ is the volume fraction of the penetrant, and V ₁ represents the penetrant partial molar volume.

$\begin{matrix} {\frac{G_{11}}{{\overset{\_}{V}}_{1}} = {{- {\left( {1 - \phi_{1}} \right)\left\lbrack \frac{\partial\left( {a_{1}\text{/}\phi_{1}} \right)}{\partial a_{1}} \right\rbrack}_{p,T}} - 1}} & (6) \end{matrix}$

The quantity ϕ₁G₁₁/V ₁ represents the number of penetrant molecules in a cluster in excess of single, isolated penetrant molecules. Consequently, this parameter is typically non-zero at high activity and approximately zero at low activities, where clustering is less common. As mentioned previously, both clustering and plasticization phenomena exhibit an upturn in solubility at high activities. Equation 6 can be used to detect a departure from ideality and the onset of plasticization or clustering as indicated by values of ϕ₁G₁₁/V ₁ greater than zero. Application of Equation 6 to the sorption data from FIG. 2 for both polyesters is provided in FIG. 5.

From FIG. 5, it is evident that the onset of either clustering or plasticization occurs at an activity of ˜0.6 for both polyesters. Caution should be emphasized regarding the physical interpretation of FIG. 5 as definite proof for the presence of clustering, as some have found notable differences between the results from this methodology and other techniques, such as FTIR [51]. Analysis of the diffusion coefficient behavior vs. activity for both PEF and PET can help distinguish between clustering and plasticization. Detailed kinetic data reported in Part 2 reveal that both PEF and PET exhibit increasing diffusion coefficients with increasing concentration over the entire activity interval, which is consistent with the notion of plasticization [14]. However, as noted above, it is still a possibility that both clustering and plasticization could be occurring simultaneously.

Additional differentiation between the clustering and plasticization phenomena can be obtained by examining the permeability vs. activity dependence for both polyesters [49]. While not measured in this disclosure, various researchers have reported both an activity independent permeability [41] and a slight increase in permeability at high activity for semicrystalline PET [40, 70]. The latter behavior is consistent with increased chain mobility resulting from the onset of plasticization in the amorphous environment at high activity; however, the presence of impermeable crystallites may dampen the magnitude of the permeability increase due to reduction of the amorphous fraction which is available for plasticization. Regardless, the permeability increase resulting from plasticization in amorphous PET is not expected to be large due to the minor positive correlation between diffusion coefficient and activity reported elsewhere [14]. Currently, to our knowledge, there exists no literature report on the water permeability in PEF vs. activity. The diffusion coefficient for water in PEF slightly increases with increasing activity, thereby suggesting the possibility of plasticization. However, independent permeability measurements are needed to verify the presence or absence of either clustering or plasticization.

Agreement between solubility coefficients obtained from both permeation time lags and independent sorption measurements also indicate the absence of clustering [34], since the entirety of the sorbed penetrant population contributes to the permeation process. Such agreement has been observed for semicrystalline PET by multiple researchers [40, 41], and thus corroborates the evidence that plasticization is occurring in PET.

3.3 Hysteresis

Sorption hysteresis occurs when the penetrant sorption and subsequent desorption cycles do not superimpose, and can occur in a wide variety of penetrant-material combinations [71-73]. Various studies have linked hysteretic behavior to swelling of the polymer matrix, where the chains irreversibly relax to incorporate the extra penetrant at high concentrations [18, 32, 39, 74, 75]. Time-dependent non-Fickian relaxations induced by this swelling have been directly observed in Part 2 at high water vapor activities (cf. FIGS. 4 and 5 in [14]).

This disclosure demonstrates that water uptake in both PEF and PET exhibited distinct hysteresis between sorption and subsequent desorption cycles. This behavior correlates with the upturn in concentration vs. activity for both polyesters in FIG. 2 and the presence of non-Fickian relaxations at high activities [14]. Initial sorption/desorption data measured using the automated VTI instrument up to 0.95 activity for PEF and PET at 35° C. are provided in FIGS. 6 and 7, respectively, where the solid circles represent sorption and the hollow circles represent subsequent desorption. The samples were dried at 45° C. after completion of the first cycle, and followed by a second sorption/desorption cycle, which consisted of fewer data points (filled and hollow triangles for the second sorption and desorption cycle, respectively).

Dual-mode model parameters for both sorption (from 0-0.6 activity) and desorption data (from 0.95-0 activity) are provided in Table 2 for both polyesters. The Langmuir affinity parameter (b) is associated with the thermodynamic polymer/penetrant interactions, and is not expected to change during the sorption process. Consequently, values of b obtained from the initial sorption isotherms were fixed when calculating the model parameters for desorption. Inspection of the parameters in Table 2 reveals that both k_(D) and C_(H)′ for desorption are larger when compared to the respective sorption values for both polyesters. Such behavior can be understood as reflecting morphological changes in the glassy matrix resulting from swelling. Larger values of C_(H)′ are consistent with an increase in either number and/or approximate size of the Langmuir microvoids, and as a result, represent an increase in free volume in the swollen samples. The increased water sorption capacity is readily observed by the upturn in concentration vs. activity in FIG. 2. Quantitative interpretation of the classic dual-mode parameters for sorption and subsequent hysteretic desorption suggest that the glass has been conditioned to a different non-equilibrium state before and after exposure to the maximum conditioning activity. As a result, the dual-mode parameters for desorption should be considered approximate, and are included in Table 2 for completeness.

The desorption trajectory and degree of hysteresis for both polyesters is directly related to the maximum value obtained during initial sorption, as observed in the acetonitrile/cellulose acetate system in other works [32, 74]. Hysteresis is not expected to occur appreciably in the water/polyester systems for initial sorption values up to ˜0.6 activity, which marks the transition between dual-mode and plasticization behavior (cf. FIG. 5). The presence of simple Fickian diffusion up to ˜0.6 activity corroborates this notion, as observed in FIGS. 4 and 5 from Part 2 [14].

A second sorption/desorption cycle using larger sorption intervals was performed after drying both polyesters at 45° C. to investigate the permanence of the morphological changes. Resorption values in both polyesters at 0.3 and 0.6 activity (solid triangles in FIGS. 6 and 7) exhibit an increase in sorption capacity when compared to the initial sorption isotherm (solid circles), which is consistent with sorption in the increased free volume in the conditioned samples compared to the virgin samples. These results also suggest that the timescale of free volume collapse is slower than the experimental sorption experiments, thereby corroborating the observation of predominantly Fickian kinetics over the entire activity range during desorption (cf. FIGS. 4 and 5 in [14]). The resorption data points are slightly reduced when compared to the initial desorption isotherms (hollow circles). Such behavior suggests that the morphological changes induced during swelling of the glassy matrix at high activity are only semi-permanent and that deswelling is indeed occurring. Resorption values at 0.95 activity for both polyesters (solid triangles) are approximately equal to the initial sorption values at 0.95 activity (solid circles), and the subsequent desorption values for both cycles (hollow circles, hollow triangles) are satisfyingly similar. These results corroborate the notion that the desorption trajectory is dependent on the maximum sorption level achieved. Similar hysteretic behavior to that observed in the current disclosure (FIGS. 6 and 7) has been reported for multiple polymer/penetrant systems [39, 45-47, 68].

A recent study by Visser and Wessling [76] illustrates the importance of volume dilation in determining the onset of sorption-induced relaxations in Matrimid polyimide. The authors show how any gas, even relatively inert gases such as Krypton, can cause non-Fickian sorption relaxations above a threshold volume dilation. Equation 7 can be used to estimate the swelling (volume change, ΔV) of a polymer sample based on the change in sample thickness (l) [74, 77], with the assumption that the sample is an isotropic medium. In Equation 7, V₀ and l₀ represent the volume and thickness of the pure, dry polymer, respectively.

$\begin{matrix} {\frac{\Delta\; V}{V_{0}} = {\left\lbrack {\left( \frac{l}{l_{0}} \right)^{3} - 1} \right\rbrack = \left\lbrack {\left( {1 + \frac{\Delta\; l}{l_{0}}} \right)^{3} - 1} \right\rbrack}} & (7) \end{matrix}$

Calculation of swelling data via Equation 7 was only possible using the thick samples from sorption testing in liquid water. Thickness values were measured on both dry samples prior to sorption testing, and again after sorption equilibrium was achieved. Values for the percent change in thickness and volume change are provided in Table 3 for both PEF and PET, along with the final concentration of water at unit activity. At least four different samples were measured for both PEF and PET, and the uncertainty limits originate from the standard error. In the context of Visser and Wessling [76], a threshold dilation of ˜1.2% was found for the onset of non-Fickian relaxations for various gases in Matrimid. This threshold value will vary for different polymers; however, the swelling values for PEF and PET at unit activity in Table 3 are unmistakably above the respective unknown threshold limits. The swelling data reported in Table 3 also allows calculation of the partial molar volume for water in both polyesters, denoted by V, via Equation 8 [57].

TABLE 3 Swelling values for amorphous PEF and PET at 35° C. in liquid water calculated from Equation 7. Conc. at a = 1 Δl/l₀ ΔV/V₀ (cm³STP/cm³Poly) (%) (%) PEF 33.4 ± 0.1 1.3 ± 0.3 4.1 ± 0.8 PET 19.8 ± 0.1 0.8 ± 0.2 2.4 ± 0.6

$\begin{matrix} {\overset{\_}{V} = {\left( \frac{\partial V}{\partial n} \right) \approx \left( \frac{\Delta\; V}{\Delta\; n} \right)}} & (8) \end{matrix}$

Values of V obtained for PEF and PET are 27.5±5.6 cm³/mol and 26.9±6.3 cm³/mol, respectively, which are both larger than the molar volume of pure, liquid water (˜18 cm³/mol). Such seemingly anomalous behavior can be explained by three possibilities: 1) that plasticization at high activity in the polymer matrix is creating extra free volume which, in fact, is unoccupied by water molecules, thus resulting in a disproportionate volume change for the polymer/water “mixture” compared to the true amount of water added in the system, 2) the thickness measurements are not accurate enough to estimate the true values of V, or 3) the assumption of an isotropic medium for both polyesters is inaccurate. Due to the large uncertainty limits reported in the values of V for both polyesters, it is believed that option 2 likely reflects reality. Consequently, ellipsometry or other techniques more suited to performing dilation measurements should be used to verify the data reported in Table 3 for both polyesters.

3.4 Enthalpy of Sorption

In addition to the equilibrium sorption measurements at 35° C., uptake values were also measured at 0.2 activity and 15, 25, and 45° C. for water in both polyesters. Kinetic uptake data between 0.1-0.2 activity are discussed in Part 2 [14], which also reports estimates for the activation energy of diffusion and activation energy of permeation for water in PEF and PET. Measurements were recorded at 0.2 activity on virgin films to ensure dual-mode behavior applied and to avoid the upturn in concentration observed in FIG. 2 at high activity. The van't Hoff relationship in Equation 9 can describe the temperature dependence of the equilibrium uptake data, where ΔH_(S) is the effective enthalpy of sorption (kJ/mol), R is the universal gas constant, and S₀ is the pre-exponential factor. Uptake data at 0.2 activity and 15, 25, 35, and 45° C. are plotted in FIG. 8 for PEF (diamonds) and PET (circles), where the lines represent the respective model fit from Equation 9. The uncertainty limits for the ΔH_(S) values depicted in FIG. 8 originate from the standard error of the model fit. S=S ₀ exp(−ΔH _(S) /RT)  (9)

The data in FIG. 8 exhibit excellent linearity for both polyesters, and produce estimates of ΔH_(S) which are quite similar in magnitude to the enthalpy of condensation for pure water [78]. Such behavior is not surprising, and indicates that the overall enthalpy of sorption is dominated by the exothermic contribution from the enthalpy of condensation [36]. The remaining contribution from the enthalpy of mixing is therefore rationalized to be small. Values of ΔH_(S) for water in PET from the literature are sparse and variable [26, 42, 79], while no additional data exists in the literature for PEF. Values of ΔH_(S) can be estimated from the Hildebrand equation [80]; however, predictions which utilize the solubility parameter for water are not recommended due to the likelihood of non-ideal behavior [44].

4. Summary

The current disclosure examines the equilibrium water uptake properties of amorphous PEF and PET at 35° C. over the entire water activity range, with the corresponding kinetic uptake data reported in Part 2 [14]. Water sorption values were measured using the following activity ranges and techniques: 1) 0-0.6 activity with the McBain quartz spring technique, 2) 0-0.95 activity with the automated TA VTI-SA+ sorption apparatus, and 3) at unit activity using samples immersed in liquid water, with the water uptake determined using a microgram balance. A consistency check was provided through excellent agreement in the uptake data measured from all three independent methods.

PEF exhibits higher equilibrium water uptake compared to PET over the entire activity range. This behavior is attributed to the higher affinity between water and the polar furan ring vs. the non-polar phenyl ring in PET. A lower average value of the Flory-Huggins interaction parameter (χ) for PEF compared to PET also indicates a higher degree of compatibility between water and PEF. Dual-mode sorption behavior was observed at low water activity, and the onset of water plasticization occurred at approximately 0.6 activity for both polyesters as determined through a Zimm-Lundberg type analysis [69]. Verification of penetrant plasticization at high activity is provided elsewhere [14], and is evidenced by the positive correlation between diffusion coefficients and increasing activity for both polymers. Further verification between either plasticization or clustering behavior will require permeation experiments at high activity, which were not conducted in these studies. Additional complementary data and related discussions regarding the kinetic uptake analogy of the current disclosure are provided in Part 2 of this disclosure [14].

The current section (Part 1), in combination with Part 2 [14], presents the first detailed report of water sorption in PEF compared to PET. Such information is needed to advance the large-scale commercialization of PEF for a variety of markets. A future publication will discuss additional data regarding water uptake properties for both polyesters, with emphasis on the resultant thermal and mechanical properties of the dry and hydrated samples.

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Part 2. Kinetic Sorption

Overview

Diffusion coefficients for water in amorphous poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET) were studied at 35° C. over the entire water activity range. PEF exhibits a ˜5× reduction in diffusion coefficient averaged over the entire concentration interval compared to PET. Fickian diffusion was observed for water in both polyesters up to ˜0.6 activity, after which the presence of non-Fickian relaxations required treatment using the Berens-Hopfenberg modeling framework. Penetrant plasticization at high activity was found for both PEF and PET, as evidenced by a positive correlation between diffusion coefficient and increasing water concentration. Arrhenius interpretation of diffusion coefficients measured at 15, 25, 35, and 45° C. allowed calculation of the activation energies of diffusion for PEF and PET, which were similar at 47.1±2.8 kJ/mol and 46.4±3.0 kJ/mol, respectively. This disclosure goes beyond prior work pertaining to the equilibrium water sorption properties in both polyesters, and subsequently provides a detailed investigation of the water diffusion process in these materials.

5. Introduction

Studies involving water transport in polymeric materials are important, since most polymers will realistically encounter humid environments at some point during their usable lifetime. Such transport data are particularly important for materials which will be in direct contact with liquid water, since water at unit activity can cause undesirable plasticization and swelling effects in a wide variety of polymers [1-4].

Recent innovation by Avantium (The Netherlands) has enabled economical, large-scale production of 2,5-furandicarboxylic acid (FDCA), which is one of two monomers needed to manufacture poly(ethylene furanoate) (PEF). Integration of PEF into the global polyester market is desirable, due to renewable sourcing of the monomers and the largely improved barrier, mechanical, and thermal properties compared to PET [5]. Multiple studies have focused on various aspects of PEF synthesis and/or material property characterization [6-11], however, no data exist in the literature regarding the fundamental water transport properties. Applications of PEF in the beverage and food packaging industry involve high humidity environments, and knowledge of the water transport properties at ambient temperature is therefore required for accurate shelf-life predictions.

In comparison to PET, this disclosure demonstrates that PEF exhibits ˜5× reduced water diffusion coefficients averaged over the entire concentration interval. This reduction is attributed to fundamental differences in segmental mobility, which originate from the rigid furan moiety in PEF compared to the mobile phenyl moiety in PET [5]. The results from the current disclosure can be compared to the diffusion of water in poly(ethylene naphthalate) (PEN), which exhibits somewhat analogous rigidity to PEF due to hindered flipping of the bulky naphthalene moiety [12]. Rueda and Varkalis report a ˜3.2× reduction in diffusion coefficient for PEN compared to PET, where both polymers are amorphous and in the hydrated state [13]. Interestingly, the authors also report a higher equilibrium sorption in PEN compared to PET due to differences in free volume [13, 14], although the disparity in equilibrium uptake is not as significant as in the present disclosure comparing PEF to PET [15].

In an aspect, this disclosure presents a detailed kinetic investigation of water diffusion in amorphous PEF and PET, and goes beyond prior work regarding equilibrium sorption properties for water [15], oxygen transport [16], and fundamental segmental mobility [5]. Similar to the Part 1 section [15], gravimetric sorption experiments were performed using three independent techniques, thereby allowing verification of the reported diffusion coefficients. Concentration dependent diffusion coefficients are presented for amorphous PEF and PET at 35° C. over the entire water activity range, and exhibit plasticization type behavior as evidenced by the positive correlation with increasing activity. The presence of non-Fickian relaxations at high activity is consistent with this notion, as is the sorption/desorption hysteresis observed for both polyesters reported in Part 1 [15]. Additional measurements of the activation energy of diffusion can be combined with the enthalpy of sorption measurements provided elsewhere [15], thereby allowing a means to estimate the activation energy of water permeation in both polyesters. Similar calculations involving the diffusivity and solubility reveal a reduction in permeability of ˜2.8× averaged across the entire concentration interval for PEF compared to PET, which is consistent with the reduction of ˜2× for PEF vs. PET reported by Avantium [17]. This disclosure, in combination with the equilibrium sorption counterpart [15], presents the first detailed analysis of water transport in PEF and demonstrates its specific utility.

6. Experimental

6.1 Materials and Sorption Measurements

Virgin poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET) were provided by The Coca-Cola Company, and are characterized in previous works [5, 15, 16]. Repeat structures for both polyesters are shown in Table 4. Amorphous films were prepared using the same melt-press/quench methodology described in prior work [5]. Nitrogen carrier gas (Airgas, Radnor Pa.) was utilized by the TA-VTI SA+ sorption instrument, and de-ionized water was used for all sorption experiments.

TABLE 4 Poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET) repeat structures. Polymer Structure PEF

PET

6.2 Sorption Measurements

Water uptake data between 0-0.95 activity were measured during sorption and subsequent desorption for both polyesters using an automated TA VTI-SA+ vapor sorption analyzer (TA Instruments, New Castle, Del.). In this system, the desired vapor concentration is obtained via mixing of separate wet and dry nitrogen streams, which are automatically controlled by the instrument via two separate mass flow controllers. Feedback is provided to the instrument from a dew point analyzer, which continually measures the water content in the stream. The sample mass is constantly monitored via a microgram balance, after which equilibrium is realized when no change in mass is observed versus time. Additional details regarding this technique are provided in Part 1 of this disclosure [15].

Two additional gravimetric methods, i.e. the McBain quartz spring technique [18] and gravimetric liquid water method, were used to verify and corroborate the measurements recorded by the automated VTI instrument. The former technique is more suitable to testing at low vapor activities, while the latter provides uptake data at unit activity. Additional details are provided in Part 1 of this disclosure [15].

7. Results and Discussion

7.1 Diffusion Model Development

Gravimetric water sorption values are typically reported in units of weight percent water (wt %, g H₂O/g dry polymer), and can be converted via Equation 10 to a non-dimensional form useful for extracting kinetic information.

$\begin{matrix} {{\frac{M_{t}}{M_{\infty}}(t)} = \left( \frac{{m(t)} - m_{initial}}{m_{final} - m_{initial}} \right)} & (10) \end{matrix}$

In Equation 10, M_(t) represents the water uptake at time t, M_(∞) is the water uptake at equilibrium (i.e. infinite time), m is the sample mass measured by the balance, initial represents the beginning of the sorption interval, and final represents the end of the sorption interval. The M_(t)/M_(∞) parameter in Equation 10 therefore represents a normalized, non-dimensional quantity that varies from zero to unity.

Solutions of the time-dependent diffusion equation have been widely tabulated for diffusion cases involving an infinite sheet geometry and a variety of boundary and initial conditions [19]. The simplest solution is obtained via implementing a constant initial concentration throughout the film (i.e. C=C₀ at t=0) and a constant concentration at the film surfaces for t>0 (i.e. C=C₁ at x=±½ for t>0, where l is the film full-thickness). Solution using these conditions is provided in Equation 11 [19], where the subscript “F” denotes the Fickian solution, D_(Avg) (cm²/s) is the effective diffusion coefficient averaged over the concentration interval, and l (cm) is the film full-thickness.

$\begin{matrix} {{\frac{M_{t}}{M_{\infty}}}_{F} = {1 - {\sum\limits_{n = 0}^{\infty}{\frac{8}{\left( {{2n} + 1} \right)^{2}\pi^{2}}{\exp\left( \frac{{- {D_{Avg}\left( {{2n} + 1} \right)}^{2}}\pi^{2}t}{l^{2}} \right)}}}}} & (11) \end{matrix}$ Equation 11 accurately describes the kinetic sorption behavior of relatively non-condensable gases in polymer materials (i.e. O₂ in PEF [16]) and some vapors at low activity [20, 21], consistent with the validity of the boundary and initial conditions in these applications. Equation 11 can also describe the water sorption data measured by the quartz spring system in the analysis of the present disclosure (cf. FIG. 9, discussed later in the document). As mentioned previously, D_(Avg) in Equation 11 represents the average “effective” diffusion coefficient over the specified concentration interval. Mathematical representation of this average is presented in Equation 12 [22]. Consequently, D_(Avg) values reported in this paper are plotted at the midpoint of the respective sorption intervals.

$\begin{matrix} {D_{Avg} = \frac{\int_{C_{1}}^{C_{2}}{D_{eff}{dC}}}{C_{2} - C_{1}}} & (12) \end{matrix}$

Uptake data measured from the automated VTI instrument at low activities could not be accurately described by the Fickian model from Equation 11. All data recorded from this instrument exhibited a slight but distinct curvature convex to the time axis at short times, before approaching Fickian-like behavior at longer times (cf. FIG. 11, discussed later in the document).

The anomalous kinetics result primarily from a lag introduced by the process control scheme employed by the instrument. Recall that the VTI instrument produces a desired water concentration by mixing a dry nitrogen stream with a completely humidified stream and selectively controlling the respective flow rates using two separate mass flow controllers. After uptake equilibrium is achieved at the current water activity, the instrument automatically adjusts the flow rates of the wet and dry streams to produce the next desired activity. The automated control scheme obtains feedback from the measured water content determined by a dew point analyzer. Upon any activity change (sorption or desorption), the instrument will initially adjust the wet/dry flow rates to obtain a first guess for obtaining the new set-point activity. With the new flow rates held constant, the instrument then averages multiple activity readings over a discrete period of time (˜1 min). If the averaged activity is different from the set-point after this period, the instrument implements a small change to the wet/dry flow rates, and the process is repeated until the set-point activity is achieved. While the system typically achieves the desired set-point after only a few minutes, this variability is enough to produce anomalous sorption kinetics.

The sigmoidal sorption data from FIG. 11 (discussed later in the document) can be modeled formally using the Long and Richman formulation of the time-dependent boundary condition shown in Equation 13, which states that the equilibrium concentration at the film surface (C₁) is described by an exponential approach to equilibrium [23].

$\begin{matrix} {{C\left( {{\pm \frac{1}{2}},{t > 0}} \right)} = {C_{1}\left( {1 - {\exp\left( {- \frac{t}{\tau_{S}}} \right)}} \right)}} & (13) \end{matrix}$

In Equation 13, τ_(S) is the time constant used for obtaining equilibrium saturation at the film surface, and in the current disclosure, represents an instrumental parameter related to how fast the control scheme in the VTI system can implement a step-change in concentration. Solution of the time-dependent diffusion equation with the boundary conditions in Equation 13 is provided in Equation 14 [19, 23], where l is the film thickness and the subscript “F-Exp” denotes the Fickian solution obtained after application of the exponential-type boundary condition.

$\begin{matrix} {{\frac{M_{t}}{M_{\infty}}}_{F - {Exp}} = \left\lbrack {1 - {{\exp\left( {- \frac{t}{\tau_{S}}} \right)}\left( \frac{4\tau_{S}D_{Avg}}{l^{2}} \right)^{1/2}{\tan\left( \frac{l^{2}}{4\tau_{S}D_{Avg}} \right)}^{1/2}} - {\frac{8}{\pi^{2}}{\overset{\infty}{\sum\limits_{n = 0}}\frac{\exp\left( {{- {D_{Avg}\left( {{2n} + 1} \right)}^{2}}\pi^{2}\frac{t}{l^{2}}} \right)}{\left( {{2n} + 1} \right)^{2}\left( {1 - {\left( {{2n} + 1} \right)^{2}\left( \frac{\tau_{S}D_{Avg}\pi^{2}}{l^{2}} \right)}} \right)}}}} \right\rbrack} & (14) \end{matrix}$

A useful feature regarding Equation 14 is that the original Fickian solution (Equation 11) is recovered when τ_(S)=0, thereby signifying an instantaneous approach in surface concentration to the final equilibrium value (i.e. the instrumental control scheme “guesses” the correct wet/dry flow rates on the first guess during the step-change in concentration). To reiterate, the parameter τ_(S) in the current disclosure represents an instrumental time constant and does not represent a fundamental property of the polymer. Additional applications of Equation 14 and variations thereof can be found in multiple articles in the literature [24-27]. Further experimental verification for the validity of Equation 14 is provided in the supplemental information, which provides values of D_(Avg) and τ_(S) measured using nitrogen, argon, and helium as carrier gases along with variable flow rates.

The discussion thus far has focused on simple penetrant diffusion in the absence of long-term non-Fickian relaxations. As discussed previously, such relaxations are known to occur in a wide variety of penetrant and polymer systems, and can indicate the occurrence of morphological changes in the polymer. Informative discussions regarding the physical origins of non-Fickian relaxations can be found in the works by Sanopoulou et al. [28, 29] and Crank [19]. Non-Fickian relaxations can be modeled using the formalism proposed by Berens and Hopfenberg [30], shown in Equations 15 and 16, which states that both Fickian diffusion and first-order relaxation processes exist independently and can be combined using simple linear superposition. In Equation 15, M_(t) represents the total mass uptake from both mechanisms at time t, M_(t,F) is the mass uptake from the Fickian mode, and M_(t,R) is the mass uptake from the first-order relaxation mode.

$\begin{matrix} {M_{t} = {M_{t,F} + M_{t,R}}} & (15) \\ \left. {{\frac{M_{t}}{M_{\infty}}}_{BH} = {\left\lbrack {\phi_{F}\left( \frac{M_{t}}{M_{\infty}} \right.}_{F} \right) + {\left( {1 - \phi_{F}} \right)\left( {1 - {\exp\left( {- \frac{t}{\tau_{R}}} \right)}} \right)}}} \right\rbrack & (16) \end{matrix}$

In Equation 16, ϕ_(F) represents the weighting factor which specifies the relative contribution of each uptake mode, τ_(R) is the time constant for the non-Fickian relaxations, and the subscripts “BH” and “F” represent the infinite series solutions obtained using the Berens-Hopfenberg (BH) and Fickian (Equation 11) formalisms, respectively. Additional models exist in the literature for describing diffusion/relaxation phenomenon [31-33], but none are as simple and straightforward to implement as the BH model. Moreover, the BH framework specified in Equation 16 is versatile in that the infinite series solution from the simple Fickian case (Equation 11) can be replaced with the more complex solution provided in Equation 14. The final representation used in the present disclosure is provided in Equation 17, which can effectively model both the exponential approach to steady-state concentration at the film surface (for data measured from the VTI system) and the superposition of non-Fickian relaxations at high water concentrations.

$\begin{matrix} \left. {{\frac{M_{t}}{M_{\infty}}}_{{BH} - {Exp}} = {\left\lbrack {\phi_{F}\left( \frac{M_{t}}{M_{\infty}} \right.}_{F - {Exp}} \right) + {\left( {1 - \phi_{F}} \right)\left( {1 - {\exp\left( {- \frac{t}{\tau_{R}}} \right)}} \right)}}} \right\rbrack & (17) \end{matrix}$

In the following discussions throughout the paper, Equation 17 will be referenced as the “BH-Exp” model. It is important to recognize that Equations 16, 14 and 11 can all be recovered from Equation 17 depending on the shape of the kinetic curve. For example, use of Equation 17 to model a strictly Fickian uptake curve (cf. FIG. 9, discussed later in the document) will return values of ϕ_(F)≈1 and τ_(S)≈0. Similarly, use of Equation 17 to model the kinetic data from the VTI system at low water concentrations (cf. FIG. 11, i.e. absence of non-Fickian relaxations) will return values of ϕ_(F)≈1 and τ_(S)≈0. The model in Equation 17 therefore represents a robust representation which is capable of describing a wide variety of kinetic phenomena.

Application of Equation 17 to experimental kinetic sorption data was achieved using a similar MATLAB® non-linear least squares fitting routine as described in previous work [34]. Due to the presence of four unknown parameters in Equation 17, caution should be exercised regarding the selection of “initial guess” parameters required by the non-linear least squares fitting routine and how these parameters affect the final optimized model parameters. For example, the functional form of Equation 14 (cf. FIG. 11), especially for large values of τ_(S), can resemble the sigmoidal shape of the exponential relaxation term in Equation 17. Selecting a purely non-physical initial guess of 3000 s for τ_(S) when modeling the data in FIG. 11b (which clearly has a τ_(S) on the order of 200 s), could result in the MATLAB® routine “optimizing” the solution by selecting a local minima in the solution-optimization space which exhibits no physical significance. Consequently, care should be taken to ensure that the final optimized parameters truly reflect the physical phenomena occurring during diffusion. An additional discussion regarding the selection of initial guess parameters in the MATLAB® fitting routine is provided in previous work [34].

A final note should be mentioned regarding the relative time-scales of both Fickian diffusion and first-order relaxations. Direct comparison of these parameters can be obtained via the Deborah number (De) for diffusion given in Equation 18 [35], where τ_(R) is the time constant for the first-order relaxations obtained from Equation 17, and τ_(D) is the time constant for Fickian diffusion.

$\begin{matrix} {{De} = {\frac{\tau_{R}}{\tau_{D}} = \frac{\tau_{R}}{\left( {l^{2}\text{/}D} \right)}}} & (18) \end{matrix}$

Simple Fickian behavior will be observed in the kinetic uptake data for both limiting cases where De>>1 and De<<1, while diffusion cases which involve comparable diffusion and relaxation time scales (De≈1) require treatment with a relaxation-based model (i.e. BH model). Further discussions on the Deborah diffusion number can be found in the literature [31, 35, 36].

7.2 Sorption/Desorption at 35° C. (First Cycle)

Water uptake data for both polyesters measured by the manual quartz spring apparatus at low activities can be accurately described by the simple Fickian model from Equation 11. Example quartz spring data are provided in FIG. 9 for water vapor at 35° C. in PEF (diamonds) and PET (circles), and are plotted on the same graph via normalization using a non-dimensional time (D_(Avg)t/l²)^(1/2). The solid line in FIG. 9 represents the model fit from Equation 11. Similar agreement between Equation 11 and uptake data was also observed for measurements conducted in liquid water at 35° C., and will be discussed later in section 7.3. Diffusion coefficients obtained via the quartz spring method for both polyesters are provided in the supplemental information, and exhibit excellent agreement with the values obtained from automated VTI system.

The raw kinetic sorption data measured at 35° C. from the automated VTI system are shown in FIG. 10a for PEF and FIG. 10b for PET between the activity range of 0-0.95 for sorption and subsequent desorption. First examination of FIG. 10 for both polyesters reveals a Fickian-type uptake behavior during sorption up to ˜0.6 activity, as evidenced by a functional approach to equilibrium similar to that illustrated in FIG. 9 (i.e. negligible long-term relaxations). After ˜0.6 activity, however, long-term non-Fickian relaxations are observed via a protracted incremental increase in sorption capacity. In fact, examination of FIG. 10 for both polyesters reveals that true sorption equilibrium was not reached for uptake curves between 0.6-0.95 activity during initial sorption. Implications of this reality on the final kinetic model parameters, although minor, will be discussed later in the paper. The non-Fickian relaxation behavior observed at high activity is consistent with the onset of sorption-induced morphological changes associated with plasticization and an overall increase in free volume in the conditioned samples. This behavior coincides with the positive deviation from dual-mode sorption observed in Part 1 above ˜0.6 activity [15]. Data similar to that in FIG. 10 have also been observed for kinetic water sorption in sulfonated polyimide membranes [37].

The data in FIG. 10 can be partitioned into individual sorption/desorption curves via Equation 10, thereby facilitating application of Equation 17 and extraction of model parameters. The anomalous kinetics introduced by the process control lag are not apparent in FIG. 10 due to the small magnitude of τ_(S) (minutes) compared to the time-scale of the overall experiment (days). Closer examination of the kinetic uptake data for PEF from FIG. 10a is provided in FIG. 11a for the sorption interval 0-0.1 activity and in FIG. 11b for the sorption interval 0.1-0.2 activity. The uptake data in FIG. 11 are plotted versus (time)^(1/2) to better illustrate the anomalous kinetics introduced by the control scheme lag, and both the Fickian model from Equation 11 (dashed line) and the BH-Exp model from Equation 17 (solid line) are shown in the figure for comparison. It was consistently observed during VTI operation that any concentration step starting from zero activity exhibited a much larger value of τ_(S) than if the instrument initiated a step change starting from a nonzero activity. This notion is demonstrated in FIGS. 11a and 11b , where τ_(S)=1820 s in FIG. 11a (activity step 0-0.1) and τ_(S)=214 s in FIG. 11b (activity step 0.1-0.2). Anomalous kinetic uptake curves similar to FIG. 11b have also been observed by Detallante et al. [37], who used a different automated vapor sorption system than in the current disclosure and attributed the anomalous behavior to similar variability in the water vapor concentration at the film surface.

In FIG. 11, it is apparent that the BH-Exp model from Equation 17 more accurately describes the experimental data than the ideal Fickian model from Equation 11. The model parameters for all four best fit lines in FIG. 11 are provided in the figure caption. Not surprisingly, differences between diffusion coefficients calculated from the two models are accentuated in FIG. 11a due to the larger value of τ_(S) compared to that illustrated in FIG. 11b . Furthermore, a value of τ_(S)=214 s in FIG. 11b results in only a minor correction to D_(Avg) calculated from the simple Fickian model. Values of ϕ_(F)=1 were obtained from modeling Equation 17 to the data shown in FIG. 11, thereby indicating the absence of non-Fickian relaxations over the time-scale of these experiments. Significantly larger deviations between D_(Avg) values calculated from the two models are realized when ϕ_(F)<<1, as observed in the current disclosure during sorption at high activity for both polyesters.

Individual partitioning of the sorption/desorption uptake curves depicted in FIG. 10a for PEF is provided in FIG. 12, while the corresponding curves in FIG. 10b for PET are provided in FIG. 13. Sorption/desorption curves measured over the same activity interval (i.e. 0.1-0.2 for sorption, and 0.2-0.1 for desorption) are plotted on the same respective graphs to allow for easy comparison. The solid lines in FIGS. 12 and 13 represent the BH-Exp model fit from Equation 17 to the experimental sorption data, while the dashed lines represent corresponding fits to the desorption data. Desorption data were not measured during the interval 0.1-0, and consequently, only the sorption curve between 0-0.1 activity is represented in FIGS. 12a and 13 a.

Effective diffusion coefficients (D_(Avg)) obtained from the BH-Exp model fit to the sorption/desorption data for PEF in FIG. 12 are provided in FIG. 14, with corresponding values for PET from FIG. 13 provided in FIG. 15. From these figures, it is apparent that D_(Avg) exhibits a positive correlation with increasing concentration during sorption for both polyesters, with the same behavior observed during subsequent desorption. The initial increase in D_(Avg) values up to 0.6 activity can be described by typical dual-mode behavior, and is discussed fully in the supplemental information. Above 0.6 activity, however, positive deviations from ideal dual-mode behavior correlate with increased segmental mobility resulting from penetrant-induced plasticization. This behavior is opposite to that expected for penetrant clustering, which exhibits a decrease in diffusion coefficient with increasing concentration due to the larger kinetic diameter of the diffusing species [38, 39].

Data in FIGS. 14 and 15 also reveal slightly larger D_(Avg) values for sorption compared to respective desorption values for both polyesters. This behavior is consistent when considering the positive correlation between D_(Avg) and concentration. Crank notes that sorption is typically faster than desorption when the diffusion coefficient increases with concentration [19]. Regardless, the D_(Avg) values for sorption and desorption are similar in magnitude over the entire concentration range, which is similar to the behavior observed for water diffusion in polysulfone (PSF) [40]. The trends in FIGS. 14 and 15 for PEF and PET, respectively, contrast those observed for water in polyethersulfone [41], 20% poly(vinyl pyrrolidone)/PSF [40], and water in some polyimides [42], where the latter polymers exhibit a decreasing D_(Avg) with increasing concentration for sorption at high activity due to the presence of clustering.

A more accurate estimate of the true diffusion coefficient dependence vs. activity can be obtained by averaging the diffusion coefficients obtained during sorption and subsequent desorption over the same respective interval [19, 43]. Average diffusion coefficients obtained via this method are represented by D_((s+d)/2), where s and d represent sorption and desorption, respectively. D_((s+d)/2) values corresponding to both PEF and PET are plotted together in FIG. 16 to allow for easy comparison. A note regarding this average is that the morphology of the polyester material is slightly altered after initial sorption at high activity. Recall that the sorption steps were performed in series between 0-0.95 activity, followed by the desorption steps in series between 0.95-0 activity. Morphological changes in the polymer are observed via the non-Fickian relaxations in the present disclosure and by the distinct sorption hysteresis observed in FIGS. 14 and 15 presented in the disclosure at Part 1 [15]. Values of D_((s+d)/2) for PET divided by respective values for PEF between 0-0.95 activity vary from ˜6.2 to ˜2.3 at the low and high activity limits, respectively, with an average value of 5.0 across the entire concentration range. Reduced diffusion coefficients for PEF compared to PET originate from inherent differences in segmental mobility, as described [5]. Similar diffusion coefficient behavior to that observed in FIG. 16 has been observed for both semicrystalline PET and amorphous poly(ethylene naphthalate) (PEN) [13], which exhibits similar rigidity to PEF.

The average diffusion coefficient data presented in FIG. 16 for both polyesters can also be plotted as a function of equilibrium water concentration (cm³STP/cm³Poly), which can be obtained from FIGS. 14 and 15 in Part 1 [15] for PEF and PET, respectively. Values of D_((s+d)/2) from FIG. 16 are plotted in FIG. 17 versus the average equilibrium concentration, which reflects the average concentration from beginning to end of the interval and averaged again between sorption and desorption concentrations to account for sorption hysteresis. The lines in FIG. 17 represent model fits from Equation 19, which assumes an exponential dependence for the diffusion coefficient on concentration. D=D _(∞) exp(βC _(Avg))  (19)

In Equation 19, C_(Avg) represents the aforementioned average concentration, β is a constant, and D_(∞) is the infinite dilution diffusion coefficient. Model parameters from Equation 19 for PEF are D_(∞)=1.0×10⁻⁹ cm²/s and β=0.073 (cm³STP/cm³Poly)⁻¹, while corresponding model parameters for PET are D_(∞)=9.6×10⁻⁹ cm²/s and β=0.049 (cm³STP/cm³Poly)⁻¹. Reports in the literature suggest that values for β increase with increasing penetrant size for diffusion in PET, and the value of 0.049 for PET from the current disclosure is significantly lower than values reported for ethanol, n-propanol, i-propanol, i-butane, and ethyl acetate [21, 44, 45]. Additionally, PEF exhibits a larger concentration dependence than PET as evidenced by the slightly larger value for β. Such results are consistent with the observation of Chandra and Koros [21], who suggested a positive correlation between concentration dependence and interaction between penetrant and polymer matrix. The latter notion is discussed in Part 1 [15], where water is shown to exhibit higher compatible with PEF vs. PET due to the polar furan ring.

The presence of non-Fickian relaxations during sorption at high activity (>0.6) for both polyesters is apparent via the long, protracted approach to equilibrium observed in FIGS. 10, 12, and 13. Similar non-Fickian behavior to that reported in the current disclosure has been reported by Schult and Paul [46] in their work regarding water sorption in polyethyloxazoline and polyethersulfone, and in additional studies regarding water sorption in PET [2, 47]. The onset of non-Fickian behavior in the present disclosure is best visualized by a plot of the respective ϕ_(F) values from Equation 17 for the best-fit models illustrated in FIG. 12 for PEF and FIG. 13 for PET. A plot of ϕ_(F) vs. activity during initial sorption is provided in FIG. 18a for both PEF (diamonds) and PET (circles), with the corresponding graph for desorption included in FIG. 18b . Simple Fickian diffusion is dominant during sorption up to 0.6 activity, as evidenced by ϕ_(F) values near unity for both polyesters in FIG. 18a . Alternatively, a large systematic decrease in ϕ_(F) is observed above 0.6 activity during sorption, thereby indicating a transition to relaxation-dominated mass uptake. Fickian kinetics dominate the desorption process, as observed by ϕ_(F) values near unity for both polyesters in FIG. 18b over the entire concentration range. It is also known that a slightly retarded approach to equilibrium during the final stages of desorption can accompany the specific type of concentration dependence observed in the current disclosure [19]. This protracted approach to equilibrium during desorption can also potentially result from deswelling of the previously swollen matrix, as observed by Berens [48] in the case of vinyl chloride sorption in poly(vinyl chloride) or by Bagley and Long [49] in the case of acetone sorption in cellulose acetate. Consequently, the values of ϕ_(F) not equal to unity in FIG. 18b are potentially a result of the relaxation-based model attempting to describe this deswelling process or the protracted approach resulting from the concentration dependence of the diffusion coefficient. Nevertheless, the observation of predominantly Fickian kinetics upon desorption is consistent with the notion that the collapse of extra free-volume which was introduced during sorption occurs significantly slower than the Fickian desorption process, thereby resulting in the appearance of Fickian kinetics [40, 48]. A brief discussion regarding the persistence of the morphological changes is provided in Part 1, which illustrates sorption hysteresis in both polyesters [15]. The remaining BH-Exp model parameters from Equation 17 for the best-fit curves in FIGS. 12 and 13 are provided in FIG. 19 for τ_(R) and in FIG. 20 for τ_(S).

Values of τ_(R) from Equation 17 can only be evaluated accurately via the MATLAB® modeling technique when ϕ_(F)<1. Consequently, FIG. 19 only reports τ_(R) values in conjunction with the respective ϕ_(F) parameters depicted in FIG. 18a during sorption, which are less than unity above ˜0.5 activity. Corresponding τ_(R) values for desorption are also only provided for values of ϕ_(F)<1 as reported in FIG. 18b . It is interesting to observe that both PEF and PET exhibit similar relaxation rates during sorption at high activity despite seemingly large differences in segmental mobility [5].

Values of the instrumental time constant associated with the process control lag (τ_(S)) are plotted in FIG. 20 for PEF (diamonds) and PET (circles) during both sorption (solid) and desorption (hollow). To reiterate, τ_(S) is not a fundamental polymer parameter and is employed solely to remove the anomalous behavior introduced by the instrument control lag. Consequently, τ_(S) is approximately constant during the activity range between 0.1-0.95 for both polyesters. The exception is the interval starting from zero, which consistently produced larger values of τ_(S). As a consistency check, all values of τ_(S) reported in FIG. 20 were significantly smaller than (l²/D_(Avg)), which is the respective time scale for diffusion. Automated VTI measurements using argon and helium in addition to nitrogen are provided in the supplemental information between the interval 0.1-0.2 activity to further explain the choice of Equation 17 and role of τ_(S) in the current disclosure.

As mentioned previously, extra time was allotted to allow for completion of sorption at activities greater than 0.6 (cf. FIGS. 10, 12, and 13); however, the uptake curves did not reach complete equilibrium and were still increasing when the system proceeded to the next activity step. This effect is accentuated at the highest sorption interval between 0.9-0.95 activity, which corresponds with the upswing in equilibrium vs. concentration reported in Part 1 [15]. Berens [48], who studied vinyl chloride sorption in poly(vinyl chloride), also terminated his runs before true equilibrium was reached due to excessively lengthened experiment times.

Recall that the diffusion model provided in Equation 17 represents a linear superposition of both Fickian and relaxation terms, where both are assumed to occur independently of the other [30]. Since enough time was allowed in FIGS. 12 and 13 to fully span the timescale needed for Fickian diffusion, it is possible, in theory, to obtain accurate values of the diffusion coefficient without reaching true uptake equilibrium [49]. Furthermore, not achieving true equilibrium due to the presence of relaxations should only affect the model parameters associated with the relaxation process, which are ϕ_(F) and τ_(R) in Equation 17. The end-result for the relaxation-based model parameters will be 1) a further decrease in ϕ_(F) than illustrated in FIG. 18a due to the larger contribution from the relaxation mode, and 2) an increase in τ_(R) for the values illustrated in FIG. 19 due to longer time needed for completion of the relaxation process. Only one relaxation term in the BH framework was considered in Equation 17 for simplicity and to achieve “uniqueness” in the final model parameters. It is possible, however, that additional relaxation terms in the BH framework might be needed to model the complete uptake curve in the case of achieving true equilibrium. Consequently, the relaxation parameters provided in FIGS. 18 and 19 serve the purpose of providing a workable, phenomenological description of the relaxation process in both polyesters. Continuing with the aforementioned discussion, the diffusion coefficients calculated in the absence of long-term relaxations (i.e. p/p₀<0.6 during sorption, and all activities during desorption) reflect a higher degree of confidence in the optimized values, while more uncertainty exists in the optimized values for D_(Avg) during sorption at high activity due to the large relaxation contribution from Equation 17.

7.3 Sorption/Desorption at 35° C. (Second Cycle) and Sorption at Unit Activity

The values for D_(Avg) reported in FIGS. 14 (PEF) and 15 (PET) are for initial sorption (solid circles) and subsequent desorption (hollow circles). Recall that equilibrium uptake hysteresis was detailed in Part 1 of this disclosure, which included data for a second sorption cycle to examine the persistence of the sorption-induced morphological changes (cf. FIGS. 6 and 7 in [15]). The kinetic counterpart to the equilibrium data during the second sorption cycle at 35° C. will now be presented.

Sorption during the second cycle consisted of larger concentration intervals than used initially (i.e. 0-0.3, 0.3-0.6, and 0.6-0.95 for sorption, and 0.95-0.6, 0.6-0.3, 0.3-0.05 for desorption). Values of the average diffusion coefficient from sorption and desorption (i.e. D_((s+d)/2), discussed previously) during the second cycle at 35° C. are plotted via the hollow circles at the midpoint of the concentration interval in FIG. 21 for PEF and FIG. 22 for PET. Corresponding D_((s+d)/2) values obtained during the first cycle are plotted in FIGS. 21 and 22 (hollow diamonds) for comparison. Parameter values for the additional model parameters from the BH-Exp model (Equation 17) are similar to those reported for initial sorption (cf. FIGS. 18-20), and are not included.

Inspection of the diffusion coefficients in FIGS. 21 and 22 reveals excellent reproducibility between the average values during sorption/desorption for both the initial and subsequent sorption cycles. Not shown in FIGS. 21 and 22 are the separate diffusion coefficients obtained during sorption and subsequent desorption during the second sorption cycle. In fact, these respective values for both polyesters exhibited much closer agreement than the sorption/desorption values during the initial sorption cycle reported in FIGS. 14 and 15. This notion is consistent with the work of Berens [48], who hypothesized that the diffusion coefficients obtained during sorption and desorption would eventually converge if enough sorption cycles were performed.

As mentioned previously, uptake experiments at unit activity were performed using a gravimetric liquid water method. Kinetic uptake curves resulting from this method were predominantly Fickian despite the high activity of water, due to the thickness of the films needed to ensure large, experimentally accessible timescales for diffusion. Correspondingly, Deborah numbers (De) for both polyesters were significantly less than unity (i.e. De≈0.04 for PEF, De≈0.03 for PET), so the appearance of Fickian kinetics is not surprising. Kinetic uptake curves representing data from four separate sorption experiments are provided in FIG. 23(a) for PEF and (b) for PET, and are plotted versus a non-dimensional time (D_(Avg)t/l²)^(1/2) to normalize differences in film thickness. Values for the diffusion coefficient measured during sorption (D_(Avg)) are provided for both polyesters in FIGS. 21 and 22 via the filled circles, and are plotted at the midpoint of the sorption interval (0.5 activity).

The value of D_(Avg) plotted in FIG. 21 (filled circle) for PEF exhibits excellent agreement with the corresponding diffusion coefficients measured from the automated VTI instrument. However, the respective value for PET plotted in FIG. 22 (filled circle) is slightly lower than the values measured from the VTI instrument. Diffusion coefficients measured at unit activity in the literature for amorphous PET are somewhat varied [47, 50, 51], but are similar in magnitude to the value reported in this disclosure.

7.4 Transport Energetics

In addition to the above measurements at 35° C., kinetic uptake curves were also measured at 15, 25, and 45° C. between the activity interval 0.1-0.2 for both polyesters. Equilibrium uptake data at 0.2 activity for all four temperatures are presented in Part 1 [15], which also reports estimates for the enthalpy of sorption for water in both polyesters. Measurements were performed between 0.1-0.2 activity to ensure simple Fickian diffusion (ϕ_(F)=1) and to avoid large values of τ_(S) (discussed previously) associated with the sorption interval starting from zero. The resulting kinetic uptake curves were predominantly Fickian, with correspondingly small values of τ_(S) consistent with those reported in FIG. 20. The temperature dependence of the diffusion coefficients can be described via the Arrhenius representation in Equation 20 [52], where E_(D) is the activation energy of diffusion (kJ/mol), R is the universal gas constant, and D₀ is the pre-exponential factor. Values of D_(Avg) measured at 15, 25, 35, and 45° C. are plotted in semi-logarithmic form in FIG. 24 for both PEF (diamonds) and PET (circles). The lines represent the corresponding fits from Equation 20, and the uncertainty limits for E_(D) are taken from the standard error of the model fits. D=D ₀ exp(−E _(D) /RT)  (20)

Excellent linearity is observed in the Arrhenius model fits in FIG. 24, thereby giving confidence to the E_(D) values of 47.1±2.8 kJ/mol for PEF and 46.4±3.0 kJ/mol for PET. Values of E_(D) reported in the literature for water diffusion in both semicrystalline and amorphous PET are similar to those reported in the disclosure for amorphous PET [47, 51, 53, 54], while no additional data exists in the literature for PEF. Quick inspection of the E_(D) values for PEF and PET in FIG. 24 reveals a slightly higher value for PEF; however, the uncertainty limits result in statistically indistinguishable values for both polyesters. The E_(D) values shown in FIG. 24 for water diffusion reveal distinct similarity to the respective E_(D) values for oxygen diffusion in both polyesters [16]. Such behavior is consistent with the work of Yasuda and Stannett, who reported similar E_(D) values for water and oxygen in the same polymer for rubber hydrochloride, PET, ethyl cellulose, and polypropylene [53].

Values of the effective enthalpy of water sorption (ΔH_(S)) for both polyesters are calculated in Part 1, and reflect values of −47.5±0.6 kJ/mol for PEF and −47.0±0.6 kJ/mol for PET [15]. Combination of the enthalpy of sorption with the activation energy of diffusion for both polyesters yields an estimate for the effective activation energy of permeation (E_(P)), which can be calculated via Equation 21. Estimates of E_(P) for water in PEF and PET are provided in Table 5, where the uncertainty limits originate from the standard error of the fit. E _(p) =E _(D) +ΔH _(S)  (21)

TABLE 5 Transport energetics for water in PEF and PET. Values of ΔH_(S) are calculated in Part 1 [15]. E_(D) ΔH_(S) E_(P) (kJ/mol) (kJ/mol) (kJ/mol) PEF 47.1 ± 2.8 −47.5 ± 0.6 −0.4 ± 2.8 PET 46.4 ± 3.0 −47.0 ± 0.6 −0.6 ± 3.1

Values of E_(P) reported in Table 5 exhibit small values close to zero, thereby reflecting a weak temperature dependence for water permeability in both polyesters over the measured activity range (0.1-0.2). Similar E_(P) values for semicrystalline PET are reported in the literature [55, 56]. As a reminder, the E_(P) values for both polyesters reported in Table 5 are first estimates, and will ideally be validated in the future by independent permeation tests.

8. Summary

The current disclosure investigates the kinetic uptake properties of water in amorphous PEF and PET across the entire water activity interval at 35° C., and goes beyond prior work which investigates the corresponding equilibrium uptake properties at the same conditions [15]. Uptake data was measured using three independent and complementary methodologies. Excellent agreement was observed between all three methodologies, thereby providing a consistency check for the reported data.

Simple Fickian behavior was observed for water diffusion in both polyesters up to ˜0.6 activity, after which the presence of non-Fickian relaxations required treatment with the Berens-Hopfenberg model. Anomalous curvature was introduced in all uptake data measured by the automated VTI instrument due to lag introduced by the control scheme. Such anomalous behavior was successfully accounted for via implementation of the formal diffusion model proposed by Long and Richman [23]; however, the physical significance of the parameters are totally different in the two cases. In fact, the use of the Long and Richman model in the present case is simply for the sake of convenience, while the coefficients in the original Long and Richman work related to actual molecular relaxation times.

Both polyesters exhibited a positive correlation between diffusion coefficient and increasing concentration over the entire concentration range. Diffusion coefficient data between 0-0.6 activity can be described using the partial immobilization model (cf. supplemental information), after which positive deviations from dual mode behavior indicate the likely presence of plasticization. While not bound by theory, permeation experiments may be ultimately used to further verify the presence of either plasticization or clustering at high activity in both polyesters.

PEF exhibits a significantly reduced water diffusion coefficient of ˜5× averaged over the entire concentration range compared to PET at 35° C. The reduction in diffusion coefficient for PEF vs. PET originates from the reduction in segmental mobility due to the non-symmetrical furan ring in PEF compared to the symmetrical phenyl ring in PET [5]. Additionally, the added polarity of the furan ring in PEF imparts the increased equilibrium water solubility of ˜1.8× averaged over the entire concentration range compared to PET [15]. The respective increase in solubility and decrease in diffusivity for water in PEF vs. PET can be combined using the common relationship P=DS to provide a permeability comparison for both polyesters. Multiplication of the aforementioned parameters yields an average permeability reduction of ˜2.8× for water in PEF compared to PET at 35° C. over the entire concentration interval. This value is similar to the ˜2× permeability reduction for PEF vs. PET reported by Avantium [17]. This disclosure, in combination with the Part 1 disclosure [15], provides the first detailed investigation of water transport in PEF and demonstrates its specific utility.

References

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Part 2. Kinetic Sorption—Supplemental Information

1. Diffusion Model Justification

As stated in the kinetic sorption section (Part 2) of this disclosure, uptake curves generated from the automated VTI instrument exhibited anomalous curvature at short times due primarily to lag introduced by the automated control scheme (cf. FIG. 3 in [1]). Such data were formally modeled using the framework established by Long and Richman [2], which implements an exponential approach to surface concentration at the film surface. The boundary conditions and solution to the transient diffusion equation are reproduced in Equations S1 and S2 below, where l is the film thickness, C is concentration, D_(Avg) is the effective diffusion coefficient averaged over the concentration interval, and τ_(S) is the time constant for achieving equilibrium saturation at the film surface.

$\begin{matrix} {{C\mspace{11mu}\left( {{\pm \frac{l}{2}},{t > 0}} \right)} = {C_{1}\left( {1 - {\exp\left( {- \frac{t}{\tau_{S}}} \right)}} \right)}} & ({S1}) \\ {{\frac{M_{t}}{M_{\infty}}}_{F - {Exp}} = \left\lbrack {1 - {{\exp\left( {- \frac{t}{\tau_{S}}} \right)}\left( \frac{4\tau_{S}D_{Avg}}{l^{2}} \right)^{1/2}\tan\mspace{11mu}\left( \frac{l^{2}}{4\tau_{S}D_{Avg}} \right)^{1/2}} - {\frac{8}{\pi^{2}}{\overset{\infty}{\sum\limits_{n = 0}}\frac{\exp\left( {{- {D_{Avg}\left( {{2n} + 1} \right)}^{2}}\pi^{2}\frac{t}{l^{2}}} \right)}{\left( {{2n} + 1} \right)^{2}\left( {1 - {\left( {{2n} + 1} \right)^{2}\left( \frac{\tau_{S}D_{Avg}\pi^{2}}{l^{2}} \right)}} \right)}}}} \right\rbrack} & ({S2}) \end{matrix}$

In the original application of Long and Richman [2], Equations S1 and S2 were implemented to account for non-Fickian relaxations occurring in the polymer during vapor sorption. The model parameter τ_(S) therefore represents an intrinsic property of the material, and will vary based on the penetrant/polymer system being investigated. The current disclosure differs from the original application, in that Equation S2 is implemented out of convenience to account for the lag introduced by the automated process control scheme of the VTI instrument. The automated VTI instrument operates by mixing two separate nitrogen streams, one completely humidified and the other dry, using differing respective flow rates to achieve the desired water activity. The resultant mixed stream is then split so that half flows into the chamber which contains the sample, and the other half flows into a separate reference chamber which contains an empty quartz basket. Additional details regarding operation of the VTI instrument are provided elsewhere [1, 3].

A secondary cause of the anomalous sorption kinetics observed in the current disclosure originates from variability in water concentration at the film surface due to large residence times of the carrier gas inside the sample chamber. This behavior is conceptually similar to that observed for a concentration step change in a continuous stirred tank reactor (CSTR). The residence time (τ_(Res)) for the carrier gas in the current disclosure is defined as the volume of the sample chamber (cm³) divided by the volumetric flow rate of the carrier gas (cm³/min). The volume of the chamber is estimated to be ˜152 cm³ (˜3.8×3.8×10.5 cm), and the combined wet/dry flow rate was automatically set at ˜427 cm³/min for all water activities. Calculation of the residence time for the carrier gas inside the sample chamber is straightforward and equals ˜43 s (i.e. 152/(427/2)). The value of τ_(Res) is therefore lower than the value of ˜133 s for τ_(S) averaged over the entire activity range during sorption and desorption in FIG. 20 in the kinetic sorption section (Part 2) of this disclosure, but still likely contributes to the overall anomalous kinetic behavior. Consequently, the τ_(S) parameter in Equation S2 reflects contributions from both the process control lag and the secondary residence time effects associated with a step change in water activity. Additional investigation of this notion is provided in Table S1, which lists D_(Avg) and τ_(S) data measured for water in PEF using pure helium and pure argon as the carrier gas, in addition to nitrogen operated at lower flow rates via manual control. All data in Table S1 were measured at 45° C. between the sorption interval of 0.1-0.2 activity.

TABLE S1 D_(Avg) and τ_(S) values for water in PEF measured at 45° C. during sorption between 0.1-0.2 water activity. The total flow rate reflects combination of both dry and humid streams, and is split into two separate streams before entering the sample and reference chambers. Total flow rate D_(Avg) × 10⁹ τ_(S) τ_(Res) ^(c) Carrier gas (cm³/min) (cm²/s) (s) (s) Nitrogen 427^(a) 4.0 102 ~43 213^(b) 4.0 102 ~86 106^(b) 4.2 278 ~173 Helium 427^(a) 4.2 48 ~43 Argon 427^(a) 3.9 70 ~43 ^(a)Measurements obtained using automated flow control. ^(b)Measurements obtained using manual flow control. ^(c)τ_(Res) ≈ (chamber volume)/(carrier gas flow rate in the sample chamber).

As seen from Table S1, values of D_(Avg) and τ_(S) are similar in magnitude for all cases, with the possible exception being the τ_(S) value measured using the lowest nitrogen flow rate of 106 ccSTP/min. This behavior indicates that neither the carrier gas type nor the flow rate significantly impacts the anomalous contribution to the diffusion process. Furthermore, this behavior is consistent with the notion that the process control lag is the primary cause of the anomalous sorption behavior, with residence time effects likely existing as a secondary cause. These experiments further confirm the utility of Equation S1 and S2 in the current disclosure for removal of the non-physical “instrument-induced” anomalous behavior, thereby allowing extraction of more accurate intrinsic polymer parameters.

2. Quartz Spring Diffusion Coefficient Data at 35° C.

Diffusion coefficients obtained during water sorption at 35° C. are provided in FIG. 25 for PEF (diamonds) and PET (circles) measured by the automated VTI system (solid points) and the manual quartz spring system (hollow). The D_(Avg) values in FIG. 25 are plotted at the midpoint of the sorption interval, and exhibit consistency between the two independent methods.

3. Partial Immobilization Model Interpretation

Diffusion of low-activity vapor in glassy polymers can often be described using the partial immobilization model (PIM), which assumes a different mobility exists for penetrant sorbed in the Henry's law environment compared to the Langmuir microvoids [4, 5]. The PIM representation of the diffusion coefficient averaged over a discrete interval is given in Equation S3 [6-8], where D_(D) is the diffusion coefficient for the Henry's law environment, F is the difference in penetrant mobility between the Langmuir microvoids compared to the Henry's law environment (D_(H)/D_(D)), p is the penetrant pressure at the beginning of the interval (subscript 1) and end of the interval (subscript 2), b is the Langmuir affinity parameter, and K=C_(H)′b/k_(D).

$\begin{matrix} {D_{Avg} = {D_{D}\left( \frac{1 + \frac{FK}{\left( {1 + {bp}_{1}} \right)\left( {1 + {bp}_{2}} \right)}}{1 + \frac{K}{\left( {1 + {bp}_{1}} \right)\left( {1 + {bp}_{2}} \right)}} \right)}} & ({S3}) \end{matrix}$

As discussed in the Part 1 portion of this disclosure, simple dual mode sorption behavior was observed for water at 35° C. in both polyesters up to ˜0.6 activity (cf. FIG. 1 in ref [3]). Values of the dual mode model parameters needed to evaluate Equation S3 (i.e. C_(H)′, b, and k_(D)) are provided in Table 2 of ref [3]. The parameter F can vary from zero to one, where the former represents the limit of total penetrant immobilization within the Langmuir microvoids and the latter represents no immobilization. Values of F near zero are common for condensable gas and vapor transport in PET, such as benzene [6] and methanol [9], and it is expected that corresponding parameters for water in PET and PEF will be analogously close to zero. Consequently, values of F≈0 are assumed for water transport in both polyesters in the subsequent discussions. FIGS. 26a and 26b provide diffusion coefficient data for water in PEF and PET, respectively, at 35° C. during initial sorption testing using the VTI instrument. The solid lines represent the optimized fit of Equation S3 to both respective data sets (with F≈0), where D_(D)≈2.6×10⁻⁹ cm²/s for water in PEF and D_(D)≈1.5×10⁻⁸ cm²/s for water in PET. The dashed line represents 0.6 activity (0.033 atm), which marks the departure from dual mode behavior.

As seen in FIG. 26, the departure from simple dual mode behavior occurs at ˜0.033 atm (0.6 activity) for both polyesters and is consistent with plasticization-type behavior. However, independent permeation experiments are needed to truly confirm the presence of plasticization and absence of penetrant clustering.

REFERENCES

-   1. Burgess S K, Mikkilineni D S, Yu D, Kim D J, Mubarak C R, Kriegel     R M, and Koros W J. Water Sorption in Poly(ethylene furanoate)     Compared to Poly(ethylene terephthalate). Part II: Kinetic Sorption.     Polymer 2014; Submitted. -   2. Long F A and Richman D. Concentration Gradients for Diffusion of     Vapors in Glassy Polymers and their Relation to Time Dependent     Diffusion Phenomena 1,2. Journal of the American Chemical Society     1960; 82(3):513-519. -   3. Burgess S K, Mikkilineni D S, Yu D, Kim D J, Mubarak C R, Kriegel     R M, and Koros W J. Water Sorption in Poly(ethylene furanoate)     Compared to Poly(ethylene terephthalate). Part I: Equilibrium     Sorption. Polymer 2014; Submitted. -   4. Petropoulos J H. Quantitative analysis of gaseous diffusion in     glassy polymers. Journal of Polymer Science Part A-2: Polymer     Physics 1970; 8(10):1797-1801. -   5. Paul D R and Koros W J. Effect of Partially Immobilizing Sorption     on Permeability and the Diffusion Time Lag. Journal of Polymer     Science: Polymer Physics Edition 1976; 14:675-685. -   6. Patton C J, Felder R M, and Koros W J. Sorption and transport of     benzene in poly(ethylene terephthalate). Journal of Applied Polymer     Science 1984; 29(4):1095-1110. -   7. Koros W J and Hopfenberg H B. Small Molecule Migration in     Products Derived from Glassy Polymers. Industrial & Engineering     Chemistry Product Research and Development 1979; 18(4):353-358. -   8. Koros W J, Patton C J, Felder R M, and Fincher S J. Kinetics and     equilibria of sulfur dioxide sorption in kapton polyimide. Journal     of Polymer Science: Polymer Physics Edition 1980; 18(7):1485-1495. -   9. Lee J S, Chandra P, Burgess S K, Kriegel R, and Koros W J. An     advanced gas/vapor permeation system for barrier materials: Design     and applications to poly(ethylene terephthalate). Journal of Polymer     Science Part B: Polymer Physics 2012; 50(17):1262-1270.

Accordingly, the present disclosure provides among other things for a method of plasticizing poly(ethylene furanoate) (PEF) film, the method comprising:

-   -   a) providing a poly(ethylene furanoate) (PEF) film; and     -   b) at a temperature at or below ambient temperature, contacting         the PEF film with water or high (>50%) relative humidity air for         a time period to form a plasticized PEF film.         Generally, high relative humidity air is defined as air having         over about 50% relative humidity. Additional aspects of         disclosure provide for a method of plasticizing poly(ethylene         furanoate) (PEF) by the method disclosed above, wherein the PEF         film is contacted with at least about 90% relative humidity air         at a temperature below or about ambient temperature for a time         period from about 1 h to about 40 h. Alternatively, the PEF film         can be contacted with at least about 90% relative humidity air         at a temperature below or about ambient temperature for a time         period from about 1.25 h to about 25 h; alternatively, from         about 1.25 h to about 20 h; alternatively, from about 1.25 h to         about 15 h; or alternatively, from about 1.5 h to about 12 h.         Other aspects or embodiments of this method include contacting         the PEF film with at least about 95% relative humidity air at a         temperature below or about ambient temperature for a time period         from about 0.5 h to about 50 h. Alternatively, the PEF film can         be contacted with at least about 95% relative humidity air at a         temperature below or about ambient temperature for a time period         from about 1 h to about 45 h; alternatively, from about 1.25 h         to about 35 h; or alternatively, from about 1.25 h to about         25 h. In still other aspects, the PEF film can be contacted with         at least about 95% relative humidity air at a temperature below         or about ambient temperature for a time period from about 10 h         to about 40 h.

In other aspects, the PEF film can be contacted with water at a temperature at or below about ambient temperature for a time period from about 0.25 h to about 40 h. Alternatively, the PEF film can be contacted with water at a temperature at or below about ambient temperature for a time period from about 0.5 h to about 25 h; alternatively, from about 1 h to about 25 h; alternatively, from about 2 h to about 25 h; alternatively, from about 5 h to about 25 h; alternatively, from about 0.25 h to about 25 h; alternatively, from about 0.25 h to about 20 h; or alternatively, from about 0.25 h to about 15 h.

There is also provided in this disclosure a plasticized poly(ethylene furanoate) (PEF) film made according to the methods provided herein. A method for making a poly(ethylene furanoate) (PEF) thin film is also one aspect of this disclosure, the method comprising:

-   -   a) plasticizing a poly(ethylene furanoate) (PEF) film according         to any of the methods disclosed herein to form a plasticized PEF         film; and     -   b) subjecting the plasticized PEF film to a dynamic strain         oscillation within the PEF linear viscoelastic range.         The plasticizing step can include contacting the PEF film with         at least about 90% relative humidity air at a temperature below         or about ambient temperature for a time period from about 5 h to         about 25 h; contacting the PEF film with at least about 95%         relative humidity air at a temperature below or about ambient         temperature for a time period from about 10 h to about 40 h; or         alternatively, contacting the PEF film with water at a         temperature below or about ambient temperature for a time period         from about 5 h to about 25 h. A poly(ethylene furanoate) (PEF)         thin film made according to this method is also encompassed by         this disclosure.

In some embodiments, the present disclosure provides a method of plasticizing poly(ethylene furanoate) film, the method comprising: a) having a poly(ethylene furanoate) (PEF) film; and b) contacting the PEF film with water or high (>50%) relative humidity air at a temperature greater than or equal to ambient temperature for a time period. In some embodiments, the PEF film is contacted with at least about 90% relative humidity air at a temperature greater than or equal to ambient temperature for a time period from about 1 h to about 25 h. In some embodiments, the PEF film is contacted with at least about 95% relative humidity air at a temperature greater than or equal to ambient temperature for a time period from about 0.5 h to about 50 h. In some embodiments, the PEF film is contacted with water at a temperature greater than or equal to ambient temperature for a time period from about 0.5 h to about 25 h.

In some embodiments, the present disclosure provides a method for making a poly(ethylene furanoate) thin film, the method comprising: a) plasticizing a poly(ethylene furanoate) (PEF) film according to any of the methods disclosed herein to form a plasticized PEF film; and b) subjecting the plasticized PEF film to a dynamic strain oscillation within the PEF linear viscoelastic range. In some embodiments, the PEF film is contacted with at least about 90% relative humidity air at a temperature greater than or equal to ambient temperature for a time period from about 1 h to about 25 h. In some embodiments, the PEF film is contacted with water at a temperature greater than or equal to ambient temperature for a time period from about 0.5 h to about 25 h.

In some embodiments, the present disclosure provides a process for producing an oriented, heat shrinkable film comprising: a) heating a poly(ethylene furanoate) (PEF) film above room temperature, and b) monoaxially stretching the film by an axial ratio of about 1.25:1 up to about 10:1 and/or simultaneously or sequentially biaxially stretching the film to an areal stretch ratio of about 1.25:1 to about 100:1.

In some embodiments, the present disclosure provides a process for producing an oriented, heat shrinkable film comprising: a) heating a poly(ethylene furanoate) (PEF) film above the film's glass transition temperature, and b) monoaxially stretching the film by an axial ratio of about 1.25:1 up to about 10:1 and/or simultaneously or sequentially biaxially stretching the film to an areal stretch ratio of about 1.25:1 to about 100:1.

In some embodiments, the present disclosure provides a process for producing an oriented, heat shrinkable film comprising: heating a poly(ethylene furanoate) (PEF) film prior to or during orientation in a fluid medium, wherein the heating occurs by conduction, convection, radiation (gas, air, or vacuum), or a combination thereof, and orienting the film according to any of the methods disclosed herein.

In some embodiments, a plasticized poly(ethylene furanoate) (PEF) film is made according to any of the methods disclosed herein. In some embodiments, an oriented, heat shrinkable film is made according to any of the methods disclosed herein.

In some embodiments, a PEF film is plasticized using about 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% relative humidity air. Moreover, the relative humidity percentages can be increased at a value between any of these numbers, inclusive. This parameter can be adjusted independently of or simultaneously with any other parameter. In some embodiments, a PEF film is plasticized at a temperature of about 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, or 185° C. Moreover, the temperature can be increased at a value between any of these numbers, inclusive. Moreover, the temperature can be lower than 0° C. This parameter can be adjusted independently or simultaneously with any other parameter. In some embodiments, a PEF film is plasticized over a time period of about 0.25, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, or more hours. Moreover, the time period can be increased at a value between any of these numbers, inclusive. This parameter can be adjusted independently or simultaneously with any other parameter.

Values or ranges may be expressed herein as “about”, from “about” one particular value, and/or to “about” another particular value. When such values or ranges are expressed, other embodiments disclosed include the specific value recited, from the one particular value, and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another embodiment. It will be further understood that there are a number of values disclosed herein, and that each value is also herein disclosed as “about” that particular value in addition to the value itself. In aspects, “about” can be used to mean within 10% of the recited value, within 5% of the recited value, or within 2% of the recited value.

Any headings that may be employed herein are also not intended to be used to construe the scope of the claims or to limit the scope of the subject matter that is disclosed herein. Any use of the past tense to describe an example otherwise indicated as constructive or prophetic is not intended to reflect that the constructive or prophetic example has actually been carried out.

Unless indicated otherwise, when a range of any type is disclosed or claimed, for example a range of weight percentages, processing times, and the like, it is intended that the stated range disclose or claim individually each possible number that such a range could reasonably encompass, including any sub-ranges and combinations of sub-ranges encompassed therein. For example, when describing a range of measurements such as weight percentages, every possible number that such a range could reasonably encompass can, for example, refer to values within the range with one significant digit more than is present in the end points of a range. In this example, a weight percentage between 10 percent and 20 percent includes individually 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 weight percent. Applicant's intent is that these two methods of describing the range are interchangeable. Moreover, when a range of values is disclosed or claimed, which Applicants intent to reflect individually each possible number that such a range could reasonably encompass, Applicants also intend for the disclosure of a range to reflect, and be interchangeable with, disclosing any and all sub-ranges and combinations of sub-ranges encompassed therein. Applicants reserve the right to proviso out or exclude any individual members of any such group, including any sub-ranges or combinations of sub-ranges within the group, if for any reason Applicants choose to claim less than the full measure of the disclosure, for example, to account for a reference that Applicants are unaware of at the time of the filing of the application.

In any application before the United States Patent and Trademark Office, the Abstract of this application is provided for the purpose of satisfying the requirements of 37 C.F.R. § 1.72 and the purpose stated in 37 C.F.R. § 1.72(b) “to enable the United States Patent and Trademark Office and the public generally to determine quickly from a cursory inspection the nature and gist of the technical disclosure.” Therefore, the Abstract of this application is not intended to be used to construe the scope of the claims or to limit the scope of the subject matter that is disclosed herein. Moreover, any headings that are employed herein are also not intended to be used to construe the scope of the claims or to limit the scope of the subject matter that is disclosed herein.

Any use of the past tense to describe an example otherwise indicated or understood as constructive or prophetic is not intended to reflect that the constructive or prophetic example has actually been carried out. 

We claim:
 1. A method of modifying a poly(ethylene furanoate) film, the method comprising: a) plasticizing a poly(ethylene furanoate) (PEF) film by contacting the PEF film with (1) water at a temperature at or below 25° C. for a time period from about 0.25 h to about 40 h or (2) at least about 90% relative humidity air at a temperature at or below 25° C. for a time period from about 1 h to about 40 h; and b) subjecting the plasticized PEF film to a dynamic strain oscillation within the PEF linear viscoelastic range.
 2. The method of claim 1, wherein the PEF film is contacted with at least about 90% relative humidity air at a temperature at or below 25° C. for a time period from about 1 h to about 25 h.
 3. The method of claim 1, wherein the PEF film is contacted with water at a temperature at or below 25° C. for a time period from about 0.5 h to about 25 h.
 4. A poly(ethylene furanoate) (PEF) film modified according to the method of claim
 1. 5. A method of modifying a poly(ethylene furanoate) film, the method comprising: a) plasticizing a poly(ethylene furanoate) (PEF) film by contacting the PEF film with (1) water at a temperature greater than 25° C. for a time period from about 0.5 h to about 25 h or (2) at least about 90% relative humidity air at a temperature greater than 25° C. for a time period from about 1 h to about 25 h; and b) subjecting the plasticized PEF film to a dynamic strain oscillation within the PEF linear viscoelastic range.
 6. A poly(ethylene furanoate) (PEF) film modified according to the method of claim
 5. 7. A method of modifying a poly(ethylene furanoate) film, the method comprising: a) plasticizing a poly(ethylene furanoate) (PEF) film by contacting the PEF film with at least about 95% relative humidity air at a temperature at or below 25° C. for a time period from about 0.25 h to about 50 h; and b) subjecting the plasticized PEF film to a dynamic strain oscillation within the PEF linear viscoelastic range.
 8. A poly(ethylene furanoate) (PEF) film modified according to the method of claim
 7. 9. A method of modifying a poly(ethylene furanoate) film, the method comprising: a) plasticizing a poly(ethylene furanoate) (PEF) film by contacting the PEF film with at least about 95% relative humidity air at a temperature greater than 25° C. for a time period from about 0.5 h to about 50 h; and b) subjecting the plasticized PEF film to a dynamic strain oscillation within the PEF linear viscoelastic range.
 10. A poly(ethylene furanoate) (PEF) film modified according to the method of claim
 9. 